Adaptive Two-stage Research Articles

Adaptive Two-Stage Stochastic Programming with an Analysis on Capacity Expansion Planning Problem

Problem definition: Multistage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that can be dynamically adjusted as uncertainty is realized. Often, for example, because of contractual constraints, such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of periods. Two-stage stochastic programming might be better suited to such settings, where first-stage decisions do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, named as adaptive two-stage stochastic programming, where each component of the decision policy requiring limited flexibility has its own revision point, a period prior to which the decisions are determined at the beginning of the planning until this revision point, and after which they are revised for adjusting to the uncertainty realized thus far until the end of the planning. We then analyze this approach over the capacity expansion planning problem, that may require limited flexibility over expansion decisions. Methodology/results: We provide a generic mixed-integer programming formulation for the adaptive two-stage stochastic programming problem with finite support, in particular, for scenario trees, and show that this problem is NP-hard in general. Next, we focus on the capacity expansion planning problem and derive bounds on the value of adaptive two-stage programming in comparison with the two-stage and multistage approaches in terms of revision points. We propose several heuristic solution algorithms based on this bound analysis. These algorithms either provide approximation guarantees or computational advantages in solving the resulting adaptive two-stage stochastic problem. Managerial implications: We provide insights on the choice of the revision times based on our analytical analysis. We further present an extensive computational study on a generation capacity expansion planning problem with different generation resources including renewable energy. We demonstrate the value of adopting adaptive two-stage approach against the existing policies under limited flexibility and highlight the efficiency of the proposed heuristics along with practical implications on the studied problem. Funding: This work was supported by the National Science Foundation [Grant 1633196] and the Office of Naval Research [Grant N00014-18-1-2075]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0157 .

Importance sampling enhanced by adaptive two-stage Kriging model and active subspace for analyzing rare probability with high dimensional input vector

For the high dimensional and small failure probability events widely existing in engineering, structural reliability analysis method still faces challenges at present. Since active subspace (AS) method can effectively reduce the dimension of input vector space, and metamodel-based importance sampling (IS) can efficiently estimate small failure probability, this paper combines AS with IS to propose an adaptive two-stage Kriging model method (AS-IS-AK2) for rare failure event with high dimensional problem. The proposed AS-IS-AK2 includes two stages. In the first stage, a new learning function is proposed to construct the Kriging model for roughly estimating the performance function values of all IS samples, and the gradient information is provided as a by-product for AS. In the second stage, an adaptive Kriging method is constructed in the reduced dimension space to accurately judge the states of all IS samples. Since AS reduces the dimension of input vector space, and IS reduces the required size of candidate sample pool for obtaining the convergent failure probability estimation, the computational complexity is reduced in reconstructing the Kriging model to judge the states of IS samples. The results of three examples verify the advantage of the proposed method for high dimensional problem with small failure probability.

Adaptive Two-Stage Model for Bearing Remaining Useful Life Prediction Using Gaussian Process Regression With Matched Kernels

Adaptive Two-Stage Model for Bearing Remaining Useful Life Prediction Using Gaussian Process Regression With Matched Kernels

Robust and Adaptive Two-stage Designs in Nonlinear Mixed Effect Models.

To get informative studies for nonlinear mixed effect models (NLMEM), design optimization can be performed based on Fisher Information Matrix (FIM) using the D-criterion. Its computation requires knowledge about models and parameters, which are often prior guesses. Thus, adaptive designs composed of several stages may be used. Robust approach can also be used to account for various candidate models. In the estimation step of a given stage, model selection (MS) or model averaging (MA) can be performed. In this work we propose a new two-stage adaptive design strategy, based on the robust expected FIM and MA over several candidate models. The methodology is applied to a clinical trial simulation in ophthalmology to optimize doses and time measurements. A set of dose-response candidate models is defined, and one-stage designs are compared to two-stage 50/50 designs (i.e., each stage performed with half of the available subjects), using either local optimal design or robust design, and performing analysis with one model, MS or MA. Performing a two-stage design with MS at the interim analysis can correct the choice of a wrong model for designing the first stage. Overall, starting from a robust design (1- or 2-stage) is valuable and leads to reasonable bias and precision. The proposed robust adaptive design strategy is a new tool to design longitudinal studies that could be used in different therapeutic areas.

An adaptive two-stage consensus reaching process based on heterogeneous judgments and social relations for large-scale group decision making

Large-scale group decision making is common in real-world scenarios, yet it involves two critical issues: (1) clustering individuals into subgroups according to specific criterion, and (2) facilitating any subsequent consensus reaching process. This paper presents a novel approach to address these challenges. Firstly, a set of transformation rules is proposed to convert heterogeneous judgments expressed by individuals into a homogeneous preference form. These judgments can be classified from two aspects: direct or indirect assessments, and fuzzy set or linguistic term set schemes. Subsequently, a group clustering method is introduced to classify individuals into subgroups, considering both of their preferences and social relations. The clustering method incorporates the measures of opinion divergence among individuals within the group and social network analysis techniques comprehensively. Finally, an adaptive two-stage group consensus measurement and adjustment method is proposed. The first stage employs a centralized mechanism within each subgroup, aiming to achieve intra-subgroup consensus. The second stage employs a democratic mechanism among different subgroups, focusing on inter-subgroup consensus. The effectiveness and rationality of the proposed method are demonstrated through an illustrative example and comparative analysis with state-of-the-art methods. The findings highlight the usefulness of the proposed method in addressing real-world decision-making problems within large-scale group contexts.

Adaptive Two-Stage Monte Carlo Algorithm for Accuracy Estimation of Total Least Squares

The existing theory of the total least squares (TLS) accuracy estimation contains the following problems: (1) the approximation function method based on the Taylor series expansion cannot avoid the derivative operation; (2) the selection of the number of simulations for the Monte Carlo method is subjective; and (3) the adaptive Monte Carlo algorithm is complex. Aiming at these problems, we introduce the adaptive two-stage Monte Carlo (ATMC) algorithm into the theory of accuracy estimation of the TLS. In order to consider the biases of estimation for parameters, residuals, and the estimation of the variance of unit weight, the computing process for accuracy estimation of the TLS contains bias estimation and accuracy estimation, and the algorithm is provided. In addition, based on the quasi-Monte Carlo method, an adaptive two-stage quasi-Monte Carlo (ATQMC) algorithm is proposed for the calculation of the expected bias in parameter estimates, and the algorithm flow is given. The experimental results verified the effectiveness of the ATMC and ATQMC algorithms. Compared with the ATMC algorithm, the ATQMC algorithm proposed in this paper is more efficient in the calculation of the expected bias in parameter estimates.

Adaptive Two-Stage Multisensor Convolutional Autoencoder Model for Lossy Compression of Hyperspectral Data

Adaptive Two-Stage Multisensor Convolutional Autoencoder Model for Lossy Compression of Hyperspectral Data

ATSUKF-Based Actuator Health Assessment Method for Quad-Copter Unmanned Aerial Vehicles

The actuator, which generally consists of motors, electrical regulations, and propellers, is the key component of the quadrotor Unmanned Aerial Vehicle. During the operation of the UAV, actuators are prone to degrade performance and even cause serious failure, which affects the service quality and flight safety of Unmanned Aerial Vehicles. Therefore, timely and accurate monitoring and evaluation of the health condition of actuators is of great significance to ensure the mission reliability of UAVs. This paper proposes an Adaptive Two-stage Unscented Kalman Filter-based actuator health assessment method for Quadcopter Unmanned Aerial Vehicles. Firstly, a state space equation is established based on dynamic analysis to characterize the degradation mechanism of the actuator. Then, by modifying the Two-stage Unscented Kalman Filter algorithm, the Adaptive Two-stage Unscented Kalman Filter algorithm is constructed by combining the filter divergence criterion and the covariance matching technique to implement the health assessment of actuators. Finally, experiments are carried out for different degradation scenarios to verify the effectiveness of the proposed method.

A novel adaptive two-stage approach to dynamic optimal path planning of UAV in 3-D unknown environments

A novel adaptive two-stage approach to dynamic optimal path planning of UAV in 3-D unknown environments

Global-Local Generation Adversarial Learning Based Low-Light Image Enhancement

In the field of low-light image enhancement, the existing unsupervised methods still have some problems, such as the lack of authenticity and the unclear effect of image enhancement in extremely dark conditions. To address this issue, we propose a highly-effective unsupervised approach to directly recover normal light image from low-light image by designing an effective cyclic generation adversarial network, Firstly, in order to solve the problem of insufficient memory caused by large-size input, a global and local generator has been designed. Secondly, we develop an adaptive two-stage discriminator. Among it, by discriminating the whole image, the local region that needs to be discriminated again is obtained adaptively. Finally, the loss in frequency domain is employed to avoid image distortion. We employ the focal frequency loss which allows the model to adaptively focus on frequency components that are hard to synthesize. The PI index of the method in this paper reaches on NPE, LIME, MEF, DICM and VV datasets respectively 2.81, 2.78, 2.40, 3.15, 3.69. On LOL datasets, PSNR and SSIM index reached 19.89 dB, 0.782 3, with good robustness.

An Adaptive Two-Stage Kriging-Based Infilling Strategy for Efficient Multi-Objective Global Optimization

Abstract Most practical multi-objective optimization problems are often characterized by two or more expensive and conflicting objectives, which require time-consuming simulations. Commonly used algorithms construct a surrogate model of each objective function from a few high-fidelity solutions. In order to further decrease the computational burden, adaptive infilling strategies for multi-objective problems are developed to guide the next infilling design for expensive evaluation and update the surrogate model as well as the Pareto front in an iterative manner. In this paper, a multi-objective infilling strategy integrating the Kriging model with a two-stage infilling framework is proposed, termed as ATKIS. This method allows exploitation and exploration alternately to pinpoint the infilling solution for improving the Pareto set and avoiding local over-exploitation simultaneously. At the local exploitation stage, Kriging-based prediction and uncertainty estimation are combined with Non-dominant Ranking and Minimum Relative Distance theories for determining a new design solution, which has maximum improvement relative to the current Pareto set. At the global exploration stage, Voronoi tessellation theory is employed to search for the sparsest position in the design space for a new evaluation. The proposed method is compared with five recent infilling strategies to investigate the performance of infilling ability using several numerical benchmarks. The experimental results show that the proposed method outperforms the other three strategies in improving both effectiveness and robustness using the improvement of hypervolume as the evaluating indicator. In addition, a lightweight optimization design of hoist sheaves shows that the proposed method can deal with real engineering problems, while significantly reducing the computational time and the number of expensive simulations of samples.

Optimal unplanned design modification in adaptive two-stage trials.

Adaptive planning of clinical trials allows modifying the entire trial design at any time point mid-course. In this paper, we consider the case when a trial-external update of the planning assumptions during the ongoing trial makes an unforeseen design adaptation necessary. We take up the idea to construct adaptive designs with defined features by solving an optimization problem and apply it to the situation of unplanned design reassessment. By using the conditional error principle, we present an approach on how to optimally modify the trial design at an unplanned interim analysis while at the same time strictly protecting the type I error rate. This linking of optimal design planning and the conditional error principle allows sound reactions to unforeseen events that make a design reassessment necessary.

An Adaptive Two-Stage Load Event Detection Method for Nonintrusive Load Monitoring

Load event detection is fundamental to event-based nonintrusive load monitoring (NILM) solution. It is directly related to whether the transient and steady-state signatures of appliances can be accurately extracted. In the real world, the load composition is random and complicated, the power consumption patterns of appliances are diverse, and multiple events may occur simultaneously or near each other, all these make it difficult for any one single event detection method to achieve satisfactory robustness. In coping with this, an adaptive two-stage event detection method is proposed in this article. First, an adaptive detection threshold whose value can be adjusted adaptively according to the load fluctuations is adopted, thus improving the ability to detect events of different amplitudes. Then, considering the different event geometric features, an improved edge detection method and a window-based detection method combining moving average with moving t-test are proposed for step-like events and long-transient events, respectively, and they are executed consecutively to achieve the effective capture of the complete transient process of appliances. Furthermore, an event separation step is taken to locate and separate the near-simultaneous events which often appear in low-frequency data. Specific event detection performance evaluation metrics are also designed. Comparison test results on private and public datasets show that the proposed method achieves high detection accuracy for different events of various appliances and maintains strong robustness in different operation scenarios.

A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination

For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, DE/current/1, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including DE/current/1 and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.

Adaptive Two-Stage Bregman Method for Variational Inequalities

Adaptive Two-Stage Bregman Method for Variational Inequalities

Adaptive two-stage inverse sampling design to estimate density, abundance, and occupancy of rare and clustered populations.

Sampling rare and clustered populations is challenging because of the effort required to find rare units. Heuristically, a practitioner would prefer to discontinue sampling in areas where rare units of interest are apparently extremely sparse or absent. We take advantage of the characteristics of inverse sampling to adaptively inform practitioners when it is efficient to move on to sample new areas. We introduce Adaptive Two-stage Inverse Sampling (ATIS), which is designed to leave a selected area after observation of an a priori number of only non-rare units and to continue sampling in the area when rare units are observed. ATIS is efficient in many cases and yields more rare units than conventional sampling for a rare and clustered population. We derive unbiased estimators of population total and variance. We also introduce an easy-to-compute estimator, which is nearly as efficient as the unbiased estimator. A simulation study on a rare plant population of buttercups (Ranunculus) shows that ATIS even with the easy-to-compute estimator is more efficient than its conventional sampling counterparts and is more efficient than Two-stage Adaptive Cluster Sampling (TACS) for small and moderate final sample sizes. Additional simulations reveal that ATIS is efficient for binary data (e.g., presence or absence) whereas TACS is inefficient for binary data. The overall results indicate that ATIS is consistently efficient compared to conventional sampling and to adaptive cluster sampling in some important cases.

532 - A Multicenter, Multicohort, Open-Label, Single Arm per Cohort, Phase II Study to Assess the Efficacy and Safety of Tabelecleucel in Patients with EBV-Associated Diseases Using an Adaptive Two-Stage Study Design

Background Epstein-Barr virus infection is associated with a variety of life-threatening malignant and non-malignant diseases. In immunocompromised individuals where T-cell function is impaired, loss of immune control of Epstein-Barr virus (EBV) can lead to proliferation of EBV-transformed B cells and result in immunodeficiency-associated lymphoproliferative diseases (IA-LPD). EBV-driven IA-LPDs are a heterogenous group of diseases with variable clinical and pathologic features, including primary immunodeficiency-associated LPD (EBV+ PID-LPD), acquired immunodeficiency-associated LPD (EBV+ AID-LPD), and post-transplant lymphoproliferative disorder (EBV+ PTLD). In addition, EBV-infection of mesenchymal cells can cause sarcomas, including leiomyosarcoma (EBV+ sarcoma). In rare instances, EBV viremia (ie, persistent EBV infection) can lead to non-malignant yet life-threatening complications such as chronic active EBV (CAEBV) or hemophagocytic lymphohistiocytosis (HLH). During the transition from primary EBV infection to latent state, only a subset of viral genes is expressed. The resulting latency proteins are a target of CD8+ T cells, making EBV+ malignancies good candidates for treatment with EBV-targeted cytotoxic lymphocytes. Tabelecleucel (tab-cel) is an off-the-shelf, partially human leukocyte antigen (HLA)-matched, allogeneic EBV-specific T-cell immunotherapy generated from screened EBV+ donors. Tabelecleucel is characterized by both HLA genotype and HLA restriction, the HLA allele(s) through which tab-cel exerts cytotoxic activity. Tab-cel is selected for each patient from an inventory based on the HLA restriction(s) and partial HLA matching. Initial safety and efficacy data support that tab-cel was well tolerated and showed clinical activity in patients with each of the EBV-associated diseases being proposed in study 205 [Nikiforow S et al. ESMO 2020; Kurlander LS et al. Ann Oncol 2018; Prockop S et al. JCI 2020]. These data encourage investigation to further evaluate the safety and efficacy of tab-cel in these populations. Study design and objectives This is a multicenter, multicohort, open-label, single-arm per cohort, phase II study to assess the efficacy and safety of tab-cel in patients with EBV-associated diseases (ATA129-EBV-205). The primary objective of the study is to assess the clinical benefit of tab-cel as measured by objective response rate. This study will also evaluate clinically relevant disease-specific outcomes and will characterize the safety profile of tab-cel in these patient populations. This study will enroll patients who are relapsed/refractory or newly diagnosed and ineligible for first-line therapy in the following cohorts: EBV+ AID-LPD, EBV+ PID-LPD, EBV+ sarcoma, including LMS, CAEBV/HLH and EBV+ PTLD with central nervous system [CNS]-involvement. In addition, a cohort of patients with previously untreated EBV+ PTLD where first-line therapy is not appropriate is planned to start enrollment in 2021. A Phase III study of tab-cel for solid organ or allogeneic hematopoietic cell transplant patients with EBV+ PTLD after failure of rituximab or rituximab plus chemotherapy (NCT03394365) is ongoing. Patients in each cohort will receive tab-cel in 35-day cycles. During each cycle, patients will receive intravenous tab-cel at a dose of 2 × 106 cells/kg on days 1, 8, and 15, followed by an observation period through day 35 (Figure 1). An adaptive two-stage design will be used for each cohort in this study, and for each, a maximum of eight patients will be enrolled in stage 1. The decision to move to stage 2 enrollment for any given cohort will be based on an analysis of the first eight evaluable patients in the cohort using investigator's assessment (per defined radiologic, clinical, and/or laboratory response criteria). If at least two among the first eight evaluable patients in stage 1 are responders W(ie, complete response or partial response), additional patients may be enrolled in stage 2 of that cohort. The number of patients enrolled in stage 2 will depend on the number of observed responders in stage 1 (Table 1). This design will allow for minimization of the expected number of patients required to evaluate the efficacy of tab-cel in each disease cohort independently. Figure 1. Study design schema Download : Download high-res image (589KB) Download : Download full-size image Disclosures Prockop: Jasper Pharmaceuticals: Research Funding; Mesoblast: Consultancy, Research Funding; Atara Biotherapeutics: Research Funding; Memorial Sloan Kettering: Patents & Royalties: IP related to the development of third party viral specific T cells with all of my interests assigned to MSK. Dinavahi: Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Navarro: Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Guzman-Becerra: Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Sun: Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Gamelin: Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company.

Adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer for a visible-light communication and ultra-large effective area pure silica fiber seamless integrated system

We proposed an adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer to minimize the negative influence of nonlinear distortions. A data rate of 960 Mbit/s is experimentally achieved on the guided visible-light transparent transmission over a 100-m ultra-large effective area pure silica fiber. The experimental results verified the effectiveness and improvement of the proposed method compared with the traditional feedforward post-equalizers.

A Multicenter, Multicohort, Open-Label, Single-Arm per Cohort, Phase II Study to Assess the Efficacy and Safety of Tabelecleucel in Patients with EBV-Associated Diseases Using an Adaptive Two-Stage Study Design

Background Epstein-Barr virus infection is associated with a variety of life-threatening malignant and non-malignant diseases. In immunocompromised individuals where T-cell function is impaired, loss of immune control of Epstein-Barr virus (EBV) can lead to proliferation of EBV-transformed B cells and result in immunodeficiency-associated lymphoproliferative diseases (IA-LPD). EBV-driven IA-LPDs are a heterogenous group of diseases with variable clinical and pathologic features, including primary immunodeficiency-associated LPD (EBV+ PID-LPD), acquired immunodeficiency-associated LPD (EBV+ AID-LPD), and post-transplant lymphoproliferative disorder (EBV+ PTLD). In addition, EBV-infection of mesenchymal cells can cause sarcomas, including leiomyosarcoma (EBV+ sarcoma). In rare instances, EBV viremia (ie, persistent EBV infection) can lead to non-malignant yet life-threatening complications such as chronic active EBV (CAEBV) or hemophagocytic lymphohistiocytosis (HLH). During the transition from primary EBV infection to latent state, only a subset of viral genes is expressed. The resulting latency proteins are a target of CD8+ T cells, making EBV+ malignancies good candidates for treatment with EBV-targeted cytotoxic lymphocytes. Tabelecleucel (tab-cel) is an off-the-shelf, partially human leukocyte antigen (HLA)-matched, allogeneic EBV-specific T-cell immunotherapy generated from screened EBV+ donors. Tabelecleucel is characterized by both HLA genotype and HLA restriction, the HLA allele(s) through which tab-cel exerts cytotoxic activity. Tab-cel is selected for each patient from an inventory based on the HLA restriction(s) and partial HLA matching. Initial safety and efficacy data support that tab-cel was well tolerated and showed clinical activity in patients with each of the EBV-associated diseases being proposed in study 205 [Nikiforow S et al. ESMO 2020; Kurlander LS et al. Ann Oncol 2018; Prockop S et al.JCI 2020]. These data encourage investigation to further evaluate the safety and efficacy of tab-cel in these populations. Study design and objectives This is a multicenter, multicohort, open-label, single-arm per cohort, phase II study to assess the efficacy and safety of tab-cel in patients with EBV-associated diseases (ATA129-EBV-205). The primary objective of the study is to assess the clinical benefit of tab-cel as measured by objective response rate. This study will also evaluate clinically relevant disease-specific outcomes and will characterize the safety profile of tab-cel in these patient populations. This study will enroll patients who are relapsed/refractory or newly diagnosed and ineligible for first-line therapy in the following cohorts: EBV+ AID-LPD, EBV+ PID-LPD, EBV+ sarcoma, including LMS, CAEBV/HLH and EBV+ PTLD with central nervous system [CNS]-involvement. In addition, a cohort of patients with previously untreated EBV+ PTLD where first-line therapy is not appropriate is planned to start enrollment in 2021. A Phase III study of tab-cel for solid organ or allogeneic hematopoietic cell transplant patients with EBV+ PTLD after failure of rituximab or rituximab plus chemotherapy (NCT03394365) is ongoing. Patients in each cohort will receive tab-cel in 35-day cycles. During each cycle, patients will receive intravenous tab-cel at a dose of 2 × 106 cells/kg on days 1, 8, and 15, followed by an observation period through day 35 (Figure 1). An adaptive two-stage design will be used for each cohort in this study, and for each, a maximum of eight patients will be enrolled in stage 1. The decision to move to stage 2 enrollment for any given cohort will be based on an analysis of the first eight evaluable patients in the cohort using investigator's assessment (per defined radiologic, clinical, and/or laboratory response criteria). If at least two among the first eight evaluable patients in stage 1 are responders W(ie, complete response or partial response), additional patients may be enrolled in stage 2 of that cohort. The number of patients enrolled in stage 2 will depend on the number of observed responders in stage 1 (Table 1). This design will allow for minimization of the expected number of patients required to evaluate the efficacy of tab-cel in each disease cohort independently. Figure 1. Study design schema Disclosures Prockop: Jasper Pharmaceuticals: Research Funding; Mesoblast: Consultancy, Research Funding; Atara Biotherapeutics: Research Funding; Memorial Sloan Kettering: Patents & Royalties: IP related to the development of third party viral specific T cells with all of my interests assigned to MSK. Dinavahi:Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Navarro:Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Guzman-Becerra:Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Sun:Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company. Gamelin:Atara Biotherapeutics: Current Employment, Current equity holder in publicly-traded company.

An Adaptive Two-Stage Proximal Algorithm for Equilibrium Problems in Hadamard Spaces

Equilibrium problems in Hadamard metric spaces are considered in the paper. For approximate solution of problems, a new iterative adaptive two-stage proximal algorithm is proposed and analyzed. In contrast to the previously used rules for choosing the step size, the proposed algorithm does not calculate bifunction values at additional points and does not require knowledge of the value of bifunction’s Lipschitz constants. For pseudo-monotone bifunctions of Lipschitz type, the theorem on weak convergence of the sequences generated by the algorithm is proved. It is shown that the proposed algorithm is applicable to pseudo-monotone variational inequalities in Hilbert spaces.