Interior Point Method Research Articles

A primal-dual interior-point method with full-Newton step for semidefinite optimization

A primal-dual interior-point method with full-Newton step for semidefinite optimization

Hybrid optimization for DC resistivity imaging via intelligible-in-time logic and the interior point method.

Geophysical DC resistivity imaging is crucial in subsurface exploration, environmental studies, and resource assessment. However, traditional inversion techniques face challenges in accurately resolving complex subsurface features because of the inherent nonlinearities in geophysical data. To overcome these challenges, we propose a hybrid optimization approach that combines incomprehensible but intelligible-in-time (IbI) logic with the interior point method (IPM). The IbI logic framework leverages complexity and temporal intelligibility, allowing for a dynamic interpretation of subsurface phenomena. By integrating IbI with IPM, our approach benefits from global exploration and local refinement, leading to improved convergence speed and solution quality. The objective function formulated for the inversion process includes data misfit and model regularization terms, which promote accurate and smooth solutions. Our methodology involves the use of the IbI logic algorithm (ILA) for initial global search, which identifies promising regions in the search space. This is followed by the application of IPM for local optimization. This synergy between the two algorithms ensures robustness and efficiency in handling large datasets and complex geological models. We conducted tests using synthetic and real DC resistivity data to validate our approach. The synthetic test demonstrated the accurate reconstruction of subsurface anomalies, whereas the real data test successfully identified fault zones, which is consistent with previous studies. The hybrid optimization algorithm significantly improves the resolution of subsurface structures and enhances geophysical data inversion practices. It balances the exploration and refinement phases effectively, optimizing the computation time and ensuring precise model delineation.

Advanced Applications and Methodologies in Mathematical Optimization and Operations Research: Insights into Linear Programming, Nonlinear Programming, and Decision-Making Frameworks

Mathematical optimization and operations research are pivotal disciplines in solving complex decision-making problems across industries. This research delves into advanced methodologies within these fields, with a focus on linear programming (LP), nonlinear programming (NLP), and their applications in optimizing processes and resource allocation. Linear programming, with its capacity to model and solve large-scale problems, remains a cornerstone for optimization, particularly in logistics, finance, and manufacturing. Nonlinear programming, characterized by its ability to handle complex, real-world systems with non-convex functions, expands the scope of optimization to include dynamic and intricate challenges such as energy management and machine learning. This study investigates state-of-the-art algorithms, including interior-point methods, dual simplex techniques, and gradient-based approaches, to enhance the efficiency and accuracy of solutions. By addressing theoretical advancements and practical implementations, this research bridges the gap between mathematical rigor and real-world applications. The insights gained are expected to contribute significantly to operational efficiency, strategic planning, and decision-making in diverse fields.

On the resolution of the non-smooth inverse Cauchy problem by the primal-dual method

On the resolution of the non-smooth inverse Cauchy problem by the primal-dual method

A fully probabilistic framework to compute the residual rockfall risk in presence of mitigation measures

AbstractRockfall events are expected to rise throughout the future due to climate change and extreme meteorological events. In the perspective of climate change adaptation, an accurate quantification of the risk is needed, together with a precise assessment of the effectiveness of protective measures eventually installed. All the possible block detachment scenarios together with their occurrence probability should be considered, and a time span should be selected. A fully probabilistic framework to compute the risk in absence and in presence of a protective structure is herein proposed, and a time-integrated reliability-based method, developed by the authors, is applied to define the failure probability of the protective measure. The complete method, in absence and presence of a rockfall barrier, is applied to a study case, and the residual risk in presence of the barrier is quantified. The results show the importance of considering all the possible detachment situations to have reliable results in terms of both risk and effectiveness of the protective measure quantification.

A Prospective Study on Laparoscopic Evaluation of Tubal Factors with Polycystic Ovarian Syndrome and Infertility in Bangladeshi Patients

Background: Laparoscopic evaluation plays a crucial role in assessing tubal factors in infertility cases coexisting with polycystic ovarian syndrome (PCOS). PCOS, characterized by hormonal imbalances and ovarian cysts, often leads to irregular ovulation and infertility. Laparoscopy allows for direct visualization of the fallopian tubes, identifying any obstructions or abnormalities that may hinder conception. Understanding the tubal status in PCOS-related infertility helps tailor treatment strategies, optimizing the chances of successful conception for affected couples. Objective: In this study or main goal is to evaluate the tubal factor pathology in case of infertile patients with diagnosed PCOS by laparoscopy. Method: This retrospective study was carried out at tertiary medical hospital from 2022 to 2023 where a total of 100 women who were diagnosed case of infertility with PCOS included in the study. Among these 68 % were primary infertility and 32% were secondary infertility. Results: During the study, in primary infertility 70.59% patient had no history of contraception. Only 8.82% had taken oral pill and 20.59% used barrier method. In secondary infertility had no history of contraception 25% had taken oral pill, 6.25% had taken IUCD and 6.25% used barrier method. Laparoscopic study of fallopian tube showed in primary infertility the tube of the right side was normal looking in 52 (76.47%), peritubal adhesion was present in 12 (17.65%) and hydrosalpinx was present in 4 (5.88%) cases. The tube of the left side was normal looking in 50 (73.53%), peritubal adhesion was present in 10 (14.71%) and hydrosalpinx was present in 8 (11.76%) cases. In secondary infertility the tube of the right side was normal looking in 16 (50.00%), peritubal adhesion was present 8 (25.00%) hydrosalpinx in 6 (18.75%) and the tube was absent in 2 case. In the left side the tube was normal looking in 20 (62.50%), peritubal adhesion was present in 8 (25.00%) and hydrosalpinx in ...

CRITICAL CAUSAL EVENTS IN SYSTEMS BASED ON CQRS WITH EVENT SOURCING ARCHITECTURE

Context. The article addresses the problem of causal events asynchrony which appears in the service-oriented information systems that does not guarantee that the events will be delivered in the order they were published. It may cause intermittent faults occurring at intervals, usually irregular, in a system that functions normally at other times. Objective. The goal of the work is the comparison and assessment of several existing approaches and providing a new approach for solving the causal events synchronization issue in application to the systems developed using Command Query Responsibility Segregation (CQRS) with Event Sourcing (ES) architecture approach. Methods. Firstly, the method of estimation of the likelihood of causal events occurring within the systems as the foundation for choosing the solution is suggested. Based on the results of the analysis of several projects based on CQRS with ES architecture it shows that the likelihood of critical causal events depends on the relationships among entities and the use-cases connected with the entities. Secondly, the Container of Events method, which represents a variation of event with full causality history, adapted to the needs of CQRS with ES architecture systems, was proposed in this work. The variants of its practical implementation have also been discussed. Also, the different solutions, such as Synchronous Event Queues and variation of Causal Barrier method were formalized and assessed. Thirdly, the methods described have been discussed and evaluated using performance and modification complexity criteria. To make the complexity-performance comparative assessment more descriptive the integrated assessment formula was also proposed. Results. The evaluation results show that the most effective solution of the issue is to use the Container of Events method. To implement the solution, it is proposed to make the modifications of the Event Delivery Subsystem and event handling infrastructure. Conclusions. The work is focused on the solution of the critical causal events issue for the systems based on CQRS with ES architecture. The method of estimation of the likelihood of critical causal events has been provided and different solutions of the problem have been formalized and evaluated. The most effective solution based on Container of Events method was suggested.

Nonsmooth optimization method for determining nonsmooth potential parameter in nonlinear subdiffusion equation

A determination of the nonsmooth potential parameter in a nonlinear subdiffusion model using terminal observation through a nonsmooth optimal control approach is proposed. This is achieved by converting the inverse problem to an optimal control problem with the fidelity and regularization terms in the cost functional represented by the L1 and TV norms, respectively, in order to account for the nonsmoothness of the potential. The existence of a minimizer for the optimal control problem is established and numerical solutions are obtained using the primal–dual method. The effectiveness of the proposed method is demonstrated via numerical results in comparison with the gradient descent method.

Counseling Women About Sexual Health Effects of Contraceptives.

Background: Choosing a contraceptive method is a pivotal decision for patients, whereas health care professionals (HCPs) face challenges in providing suitable recommendations. Adverse sexual effects often lead to dissatisfaction and discontinuation of contraceptives, underscoring the importance of thorough counseling and shared decision making between HCPs and patients. Objective: This article aims to investigate the relationship between contraceptive methods and female sexual function through a comprehensive review of available literature, emphasizing the importance of considering sexual health in contraceptive prescription and management. Methods: A systematic analysis of existing literature, incorporating studies utilizing validated sexual health questionnaires, was conducted to elucidate the intricate interplay between contraceptives and female sexual function. Results: The review encompasses various contraceptive methods, including combined hormonal contraceptives, progestin-only pills, depot medroxyprogesterone acetate, subdermal contraceptive implants, hormonal intrauterine devices, permanent sterilization, and barrier methods. Insights gleaned from the analysis shed light on the impact of these methods on female sexual health. Conclusion: Comprehensive understanding of the effects of contraceptives on female sexual function is crucial for both HCPs and patients. By integrating sexual health considerations into contraceptive surveillance, compliance can be improved, contraceptive efficacy optimized, and the risk of unwanted pregnancies minimized. This review underscores the significance of tailored counseling and shared decision making in contraceptive management, particularly for cisgender women.

The sexual behaviors of young Polish women and their knowledge about contraception

Introduction. With the increasing trend of early sexual activity among adolescents, contraception has become a crucial topic. Poland ranks last in the Contraceptive Atlas, as the country with the poorest access to contraception methods and information. This results in a low level of contraceptive knowledge among young people, leading to unintended pregnancies and sexually transmitted infections. Adequate sexual education is a key element in promoting sexual health, enabling informed contraceptive choices based on medical knowledge. The responsibility for sexual education lies not only with parents but also with educators, pedagogues, doctors, and governmental bodies. Aim. To assess knowledge about contraception and investigate the sexual behaviors of women aged 15-25, comparing the results with available literature and indicating possible preventive actions in the studied area. Material and methods. An anonymous electronic survey was conducted among women aged 15-25 from across Poland. The survey was distributed on various internet groups, primarily comprising students. It included closed-ended questions verifying knowledge of the topic under study and a demographic section. Statistical analysis of the data was performed using Statistica and Microsoft Excel. Results. The average age of sexual initiation among respondents was 17.84±1.96 years, with one-third of them yet to engage in sexual activity. The majority of respondents (58%) had 1 to 3 sexual partners, and with increasing age and education level, the percentage of those with a higher number of sexual partners increased. The most popular contraceptive methods among respondents were barrier methods, combined oral contraceptive pills, and a combination of barrier and hormonal methods. The main sources of contraceptive information for the respondents were the internet, gynecologists, and scientific literature. Almost all respondents were aware of the definition of contraception, but only half were aware of the Pearl Index. Less than half of the respondents could identify the most effective contraceptive method, while almost all correctly identified the least effective method. The knowledge of the majority of respondents was assessed as moderate, good, or very good. Conclusions. Despite the generally good knowledge of contraception among the majority of respondents, there are still gaps that need to be filled. Due to the progressively decreasing age of sexual initiation, education on contraception is a priority that will help reduce the number of unintended pregnancies and sexually transmitted diseases in the future.

Improvements to Quantum Interior Point Method for Linear Optimization

Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major bottleneck is the inexactness of quantum Tomography to extract classical solutions from quantum states. In addition, QLSAs are sensitive to the condition number, and this sensitivity is exacerbated when the Newton systems arising in IPMs converge to a singular matrix. Recently, an Inexact Feasible Quantum IPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs. However, this method requires a large number of gates and qubits to be implemented. Here, we propose a new IF-QIPM using the normal equation system, which requires less number of gates and qubits. To mitigate the sensitivity to the condition number and other input data-related parameters, we use preconditioning coupled with iterative refinement to obtain better complexity. Finally, we demonstrate the effectiveness of our approach on IBM Qiskit simulators.

Efficient Implementation of Interior-Point Methods for Quantum Relative Entropy

Quantum relative entropy (QRE) programming is a recently popular and challenging class of convex optimization problems with significant applications in quantum computing and quantum information theory. We are interested in modern interior-point (IP) methods based on optimal self-concordant barriers for the QRE cone. A range of theoretical and numerical challenges associated with such barrier functions and the QRE cones have hindered the scalability of IP methods. To address these challenges, we propose a series of numerical and linear algebraic techniques and heuristics aimed at enhancing the efficiency of gradient and Hessian computations for the self-concordant barrier function, solving linear systems, and performing matrix-vector products. We also introduce and deliberate about some interesting concepts related to QRE such as symmetric quantum relative entropy. We design a two-phase method for performing facial reduction that can significantly improve the performance of QRE programming. Our new techniques have been implemented in the latest version (DDS 2.2) of the software package Domain-Driven Solver (DDS). In addition to handling QRE constraints, DDS accepts any combination of several other conic and nonconic convex constraints. Our comprehensive numerical experiments encompass several parts, including (1) a comparison of DDS 2.2 with Hypatia for the nearest correlation matrix problem, (2) using DDS 2.2 for combining QRE constraints with various other constraint types, and (3) calculating the key rate for quantum key distribution (QKD) channels and presenting results for several QKD protocols. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the National Science Foundation [Grant CMMI-2347120] and Discovery Grants from the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0570 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0570 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Research on trajectory planning based on optimal control modeling

With the advancement of autonomous driving technology, trajectory planning has emerged as one of the core technologies to achieve safe and efficient vehicle driving. An algorithm for single-vehicle trajectory planning based on the Optimal Control Problem (OCP) is proposed in this paper, which can not only plan a safe and efficient path for autonomous vehicles, but also realize the obstacle avoidance function. Firstly, the OCP is modeled for the cycle trajectory planning problem. Secondly, this paper transforms it into a Nonlinear Programming (NLP) with all discrete methods, and uses the interior point method to solve it. Then, the Y-type intersection is selected as the verification scene, and through a series of simulation experiments, the efficiency and safety of the algorithm in different driving environments are verified. The model and algorithm proposed in this paper are not only applicable to Y-type intersections, but also can be extended to other complex traffic roads, providing a new idea and method for trajectory planning in intelligent transportation systems.

Obstacle avoidance control of UAV formation based on distributed model prediction

Aiming at the formation and maintenance problem of UAVs in an obstacle environment, a distributed model predictive control (DMPC) algorithm with no reference trajectory considering system constraints is proposed. In order to deal with the constraint coupling and cost coupling existing in model predictive control (MPC), the assumed trajectory is introduced to design a low conservative compatibility constraint and a cost function of no reference trajectory, so that the algorithm can be executed in a distributed and synchronous manner. Secondly, the terminal constraint is designed based on the speed barrier method to ensure the safety of the terminal domain, and a feasible terminal control input is given. The cost function is taken as a Lyapunov function, combined with the constructed stability constraint, and the iterative feasibility and system stability of the algorithm are analyzed. In addition, in order to take into account the real-time performance, a non-strictly stable DMPC algorithm that can better meet the requirements of formation obstacle avoidance is given on the basis of the proposed algorithm. The effectiveness and superiority of the proposed algorithm are verified by numerical simulation.

Proximal-stabilized semidefinite programming

AbstractA regularized version of the primal-dual Interior Point Method (IPM) for the solution of Semidefinite Programming Problems (SDPs) is presented in this paper. Leveraging on the proximal point method, a novel Proximal Stabilized Interior Point Method for SDP (PS-SDP-IPM) is introduced. The method is strongly supported by theoretical results concerning its convergence: the worst-case complexity result is established for the inner regularized infeasible inexact IPM solver. The new method demonstrates an increased robustness when dealing with problems characterized by ill-conditioning or linear dependence of the constraints without requiring any kind of pre-processing. Extensive numerical experience is reported to illustrate advantages of the proposed method when compared to the state-of-the-art solver.

Optimization control strategy for diesel urea-selective catalytic reduction (SCR) urea injection based on the interior point method (IP) + higher order SCR model

In order to ensure that the NOx and NH3 emissions of diesel engines comply with the Euro VII emission standards, this paper optimizes the urea injection using a SCR model combined with the interior point method. First, the equations of the higher-order SCR model were simplified by the variable substitution method and the line method and solved by the backward difference formula to improve computational accuracy. The Levenberg-Marquardt algorithm was used to calibrate the chemical reaction rate parameters to optimize model performance. Second, an optimization cost function was designed to optimize the upstream NH3 concentration in combination with the interior point method and the higher-order SCR model to meet the requirements of Euro VII emission standards. Third, the model effect was verified by performing WHTC hot-start testing on an engine complying with the National VI emission standard. The results show that the average error between the measured NOx concentration and the calculated is 1.49 ppm, which verifies the high accuracy of the model. Finally, the effects of the interior point method, NSGA-II, and MOPSO algorithms in optimizing the upstream NH3 concentration were compared. The results showed that the interior point method outperformed the other algorithms in terms of optimization time and effect, with an optimization time of 149 s, a NOx conversion rate of 97.36 %, and an average downstream NH3 concentration of 4.65 ppm. This achieved a high NOx conversion rate and low NH3 slip in accordance with the requirements of the Euro VII regulation.

Prediction Techniques for Dynamic Imaging with Online Primal–Dual Methods

Prediction Techniques for Dynamic Imaging with Online Primal–Dual Methods

Primal-Dual Extrapolation Methods for Monotone Inclusions Under Local Lipschitz Continuity

In this paper, we consider a class of monotone inclusion (MI) problems of finding a zero of the sum of two monotone operators, in which one operator is maximal monotone, whereas the other is locally Lipschitz continuous. We propose primal-dual (PD) extrapolation methods to solve them using a point and operator extrapolation technique, whose parameters are chosen by a backtracking line search scheme. The proposed methods enjoy an operation complexity of [Formula: see text] and [Formula: see text], measured by the number of fundamental operations consisting only of evaluations of one operator and resolvent of the other operator, for finding an ε-residual solution of strongly and nonstrongly MI problems, respectively. The latter complexity significantly improves the previously best operation complexity [Formula: see text]. As a byproduct, complexity results of the primal-dual extrapolation methods are also obtained for finding an ε-KKT or ε-residual solution of convex conic optimization, conic constrained saddle point, and variational inequality problems under local Lipschitz continuity. We provide preliminary numerical results to demonstrate the performance of the proposed methods. Funding: This work was partially supported by the National Science Foundation [Grant IIS-2211491], the Office of Naval Research [Grant N00014-24-1-2702], and the Air Force Office of Scientific Research [Grant FA9550-24-1-0343].

A robust force identification method based on L1+2-norm approximation theory

Obtaining the real force of the structure is the basic condition for efficient vibration reduction design. However, the uneasiness and instability of the inverse problem make the force identification still challenging. On the basis of L2-norm regularization, we propose a new method for force identification based on L1+2-norm approximation theory. By introducing the L1-norm penalty operator, a joint norm approximation optimization model is constructed to limit the non-zero force and punish the force value which approaching to zero, so that it can adapt to the identification of various types of forces. Then the optimal force solution is obtained by using the Primal-dual interior point method. Finally, the effectiveness and accuracy of the proposed method are verified by numerical simulation and experiment of asymmetric plate and double-layer plate structures. Different from previous studies, the L1+2-norm method in this work has high robustness, considers the characteristics of sparse regularization and L2-norm regularization, and can adapt to the identification of continuous forces and sparse forces at the same time, which has potential engineering application value.

Spatially adaptive oscillation total generalized variation for image restoration with structured textures

Cartoon and texture are the main components of an image, and decomposing them has gained much attention in various image restoration tasks. In this paper, we propose a novel infimal convolution type model based on total generalized variation (TGV) and spatially adaptive oscillation TGV to address cartoon-texture restoration problems. The proposed spatially adaptive oscillation TGV regularizer is capable of capturing structured textures with different orientations and frequencies in localized regions. Additionally, we incorporate the second-order tensor TGV to regularize the orientation and frequency parameter. The lower semicontinuity of the new functional is established and the existence of the solutions to the proposed model is analyzed. Furthermore, we discuss suitable discretizations of the proposed model, and introduce the alternating minimization algorithm where each subproblem can be implemented by the primal-dual method. Numerical experiments on image decomposition, denoising and inpainting demonstrate that the proposed model excels in preserving textures and is competitive against existing variational and learning-based models.