Interior Point Method Research Articles

Determining the Parameters of the Jones–Wilkins–Lee Equation of State of Explosives on the Basis of Data Obtained by the Barrier Method

Determining the Parameters of the Jones–Wilkins–Lee Equation of State of Explosives on the Basis of Data Obtained by the Barrier Method

Distributed inertial online game algorithm for tracking generalized Nash equilibria.

This paper is concerned with the distributed generalized Nash equilibrium (GNE) tracking problem of noncooperative games in dynamic environments, where the cost function and/or the coupled constraint function are time-varying and revealed to each agent after it makes a decision. We first consider the case without coupled constraints and propose a distributed inertial online game (D-IOG) algorithm based on the mirror descent method. The proposed algorithm is capable of tracking Nash equilibrium (NE) through a time-varying communication graph and has the potential of achieving a low average regret. With an appropriate non-increasing stepsize sequence and an inertial parameter, the regrets can grow sublinearly if the deviation of the NE sequence grows sublinearly. Second, the time-varying coupled constraints are further investigated, and a modified D-IOG algorithm for tracking GNE is proposed based on the primal-dual and mirror descent methods. Then, the upper bounds of regrets and constraint violation are derived. Moreover, inertia and two information transmission modes are discussed. Finally, two simulation examples are provided to illustrate the effectiveness of the D-IOG algorithms.

Mobile Edge Computing (MEC)-Enabled UAV Placement and Computation Efficiency Maximization in Disaster Scenario

Unmanned aerial vehicles (UAVs) are considered for disaster management to provide better coverage or help first responders provide advanced services. Furthermore, UAVs combined with mobile edge computing (MEC) capabilities, have recently emerged as a support for cloud computing by deploying UAV-assisted MEC at the network edge to reduce the latency and load of cloud computing data centers. We investigate the problem of maximizing the utility function by jointly optimizing the computing power, user associations, performance, duration, and location of user equipments (UEs) in UAV-assisted MEC networks in a disaster scenario. We considered several constraints including delay, quality of service, and coverage. The optimization problem is a mixed-integer non-linear programming problem. We propose a multi-stage offloading algorithm based on a learning algorithm and an interior-point method to obtain a viable solution. The simulation results obtained demonstrate the effectiveness of our proposed algorithm compared to existing schemes.

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

Tolerance Synthesis of Delta-like Parallel Robots Using a Nonlinear Optimisation Method

Robotic systems require high accuracy in manipulating objects. Positioning errors are influenced by geometric tolerances and various sources. This paper introduces a new technique based on the interior-point algorithm optimisation method to allocate tolerances to the geometric parameters of a robot. This method consists of three steps. First, a method for modelling the kinematic problem as well as the geometric errors must be used. The Denavit–Hartenberg rule is the most suitable method for this modelling case. Then, a mathematical model for tolerance allocation is developed and used as a nonlinear multivariable optimisation problem. Finally, the “interior-point” algorithm is used to solve this optimisation problem. The accuracy and efficiency of the proposed method, in determining the tolerance allocations for a Delta parallel robot, is illustrated via calculation and simulation results. The values of the dimensional tolerances found are optimal. As a result, these values always keep the accuracy less than or equal to the imposed value.

Practice and development of male contraception: European Academy of Andrology and American Society of Andrology guidelines.

Despite a wide spectrum of contraceptive methods for women, the unintended pregnancy rate remains high (45% in the US), with 50% resulting in abortion. Currently, 20% of global contraceptive use is male-directed, with a wide variation among countries due to limited availability and lack of efficacy. Worldwide studies indicate that >50% of men would opt to use a reversible method, and 90% of women would rely on their partner to use a contraceptive. Additional reasons for novel male contraceptive methods to be available include the increased life expectancy, sharing the reproductive risks among partners, social issues, the lack of pharma industry involvement and the lack of opinion makers advocating for male contraception. The present guidelines aim to review the status regarding male contraception, the current state of the art to support the clinical practice, recommend minimal requirements for new male contraceptive development and provide and grade updated, evidence-based recommendations from the European Society of Andrology (EAA) and the American Society of Andrology (ASA). An expert panel of academicians appointed by the EAA and the ASA generated a consensus guideline according to the GRADE (Grading of Recommendations, Assessment, Development and Evaluation) system. Sixty evidence-based and graded recommendations were produced on couple-centered communication, behaviors, barrier methods, semen analysis and contraceptive efficacy, physical agents, surgical methods, actions before initiating male contraception, hormonal methods, non-hormonal methods, vaccines, and social and ethical considerations. As gender roles transform and gender equity is established in relationships, the male contribution to family planning must be facilitated. Efficient and safe male-directed methods must be evaluated and introduced into clinical practice, preferably reversible, either hormonal or non-hormonal. From a future perspective, identifying new hormonal combinations, suitable testicular targets, and emerging vas occlusion methods will produce novel molecules and products for male contraception.

Optimization of Rectangular and Box Sections in Oblique Bending and Eccentric Compression

The article presents a solution to the problem of finding the optimal ratio of the height of the cross-section to the width for a rectangular and box-shaped section in the case of oblique bending and eccentric compression. Optimization is performed according to the strength criterion, and for the case of oblique bending of a rectangular beam, a solution was also obtained from the condition of a minimum full deflection. For a rectangular section, the solution is made analytically, and for a box section, numerically using the MATLAB environment and the Optimization Toolbox package. As a numerical method of nonlinear optimization, the interior point method is used. To simplify the solution, the box section is assumed to be thin-walled, i.e. it is assumed that the wall thickness is significantly less than the height and width of the cross section. An estimate of the error of such an assumption is also performed. It has been established that in the case of oblique bending of a rectangular beam, when optimizing according to the strength criterion, the optimal ratio of the cross-sectional height to width is equal to the cotangent of the angle between the force plane and the vertical axis, and when optimizing according to the rigidity criterion, it is the square root of the cotangent of this angle. In the case of eccentric compression of a rectangular beam with eccentricities in two planes, the optimal ratio of the height of the cross section to the width is equal to the ratio of the eccentricity along the vertical and horizontal axes. For a box-shaped section, graphs of the change in optimal parameters depending on the angle between the force plane and the vertical axis in the case of oblique bending, as well as depending on the ratio of eccentricities along the axes in the case of eccentric compression, are plotted.

Quantum Interior Point Methods for Semidefinite Optimization

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact search direction and is not guaranteed to explore only feasible points; the second scheme uses a nullspace representation of the Newton linear system to ensure feasibility even with inexact search directions. The second is a novel scheme that might seem impractical in the classical world, but it is well-suited for a hybrid quantum-classical setting. We show that both schemes converge to an optimal solution of the semidefinite optimization problem under standard assumptions. By comparing the theoretical performance of classical and quantum interior point methods with respect to various input parameters, we show that our second scheme obtains a speedup over classical algorithms in terms of the dimension of the problem n, but has worse dependence on other numerical parameters.

The role of international collaboration in the United States geologic disposal research program

Abstract. More than a decade ago, the United States disposal program discontinued all research activities focused on the unsaturated fractured tuff formation at Yucca Mountain as the geologic disposal site for spent fuel and high-level radioactive waste. A new research and development (R&D) program was initiated to provide a sound technical basis for alternative disposal options across clay, crystalline, and salt rocks. The goals of this broad program were (and still are) to (1) increase confidence in the robustness of generic disposal concepts, (2) develop the science and engineering tools needed to support disposal concept implementation, and (3) conduct R&D on the direct disposal of existing dual-purpose (storage and transportation) canisters. Recognizing the benefits of international collaboration toward the common goal of safely and efficiently managing the back end of the nuclear fuel cycle, the program emphasized international cooperation as an effective strategy for sharing information and knowledge. In a multi-laboratory effort coordinated by Lawrence Berkeley National Laboratory, the United States Department of Energy (DOE) program established formal and informal cooperation partnerships with several international initiatives and institutions and developed a number of collaborative R&D activities in important research areas, such as engineered barrier integrity, near-field perturbations, radionuclide transport, performance assessment, and methods for characterization and monitoring of engineered and natural barriers. This presentation gives an overview of these R&D activities, with a specific focus on activities that improve our current understanding of the coupled thermal–hydrological–mechanical–chemical (THMC) processes occurring in engineered and natural barriers. We start with a brief review of selected international collaboration initiatives and then describe a few specific collaboration projects. We focus specifically on such studies that use experimental data sets provided by international research cooperation for joint modeling work to increase confidence in performance-relevant predictions of coupled processes. Overall, the focus on international collaboration has allowed deep engagement of US researchers with the international waste management R&D community in terms of best practices, new scientific advances, state-of-the-art simulation tools, new monitoring and performance confirmation approaches, and lessons learned. The joint R&D with international researchers, worldwide sharing of knowledge and experience, and access to relevant data and experiments from a variety of host rocks have helped our researchers to significantly improve their understanding of the current technical basis for disposal in a range of potential host rock environments. International collaboration also provides ample opportunity for training and educating junior staff that are well suited to move the United States disposal research program forward into the next decades, a promising avenue for developing a next-generation workforce of disposal scientists.

Basement Mapping Using Nonlinear Gravity Inversion with Borehole and Seismic Constraints

We present an integrated method for mapping the basement structures of sedimentary basins by combining surface gravity data, seismic imaging, and borehole logging information. The core of the method is a nonlinear inversion algorithm for constructing the shape and depth of the basement from surface gravity data. By using the primal-logarithmic barrier method, we impose depth constraints from the borehole information. The basement depth was imaged by seismic interpretation and incorporated into the inversion as a reference model. As a result, the gravity inversion constructs basement structures that are closest to the seismic input while simultaneously satisfying the surface gravity data and borehole information. We used this new methodology to unveil the basement morphology of the Recôncavo Basin, Brazil. Recôncavo is a syn-rift onshore mature basin that exhibits a strong correlation between oil field distribution and tectonic framework. The seismic imaging in the area is ambiguous, and our approach improved the basement definition and highlighted exploration targets in the studied area.

Numerically efficient and robust interior-point algorithm for finite strain rate-independent crystal plasticity

The challenges of classic rate-independent crystal plasticity models regarding the determination of active slip systems and computation of solutions due to linear dependent slip systems are still a field of active research. In that regard, interior-point methods are promising approaches because a logarithmic barrier term naturally avoids the combinatorial active set search, and these methods are applicable even when the gradient of inequality constraints is linearly dependent. In this paper, a new interior-point algorithm suitable for rate-independent crystal plasticity at finite strains is developed. For that purpose, the postulate of maximum dissipation is recast as a constrained optimization problem whose optimality conditions are derived by utilizing interior-point approaches. This optimization problem is discretized in time by means of an exponential time integration of the flow rule, and the time-discrete equations are solved by a Newton scheme. The focus of this paper is the efficiency and robustness of the implementation of this approach. In particular, the effect of different line search procedures, favorable residual forms, preconditioning methods, barrier parameter updates and the consistent algorithmic tangent modulus are discussed and further elaborated. In addition, aspects regarding uniqueness and well-posedness of the algorithm are analyzed in a geometrically linearized setting. Efficiency and robustness of the developed algorithm are shown by numerical examples of an FCC crystal including finite element simulations without stabilizing hardening or rate-dependent effects. Furthermore, the results are compared to the well-established augmented Lagrangian formulation.

Warmstarting strategies for convex optimization based multi-channel constrained active noise control filter design

In real-world applications of active noise control (ANC) systems, various constraints are supposed to be satisfied in the controller design process. The optimal control filter coefficients can be obtained by solving a constrained optimization problem, which usually requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC filter design. The proposed formulation was shown to result in a computational time reduction by several orders of magnitude. It is of great interest to further improve its efficiency by using a priori information of the optimal filter coefficients. One potential way of achieving this goal is to introduce a warmstart technique so that the filter solution of a similar system or environment can be referred to for selecting the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method, which, in general, is challenging for applying warmstart techniques. In the current work, relaxation methods are proposed to the constraints of original ANC filter design formulation so that the warmstart techniques can be applied. Then, a warmstarting technique proposed in previous study is used to solve a series of perturbed problems, and the performance of the warmstarting technique is investigated. Results show that with the proposed modifications applied, the warmstarting strategy can significantly reduce the number of iterations needed for solving the conic formulation of the ANC filter design problem without much tuning efforts, and the method is effective and robust in various environmental setups.

Structured Static Output Feedback Mixed ${H}_2/{H}_\infty $ Control for Linear Control Systems

This note considers the design of static output feedback mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H}_2/{H}_\infty $</tex-math></inline-formula> controllers for linear control systems with certain equality and inequality constraints imposed directly on the feedback matrix. Based on the barrier method, we solve an auxiliary minimization problem to obtain an approximate solution to the original nonconvex constrained optimization problem. Necessary conditions for the optimal solution of the auxiliary minimization problem are derived using the Lagrange multiplier method. Subsequently, an iterative steepest descent algorithm is developed to find an approximate optimal solution. Finally, an example is provided to validate the proposed approach.

Accelerating Distributed Optimization via Over-the-Air Computing

Distributed optimization is ubiquitous in emerging applications, such as robust sensor network control, smart grid management, machine learning, resource slicing, and localization. However, the extensive data exchange among local and central nodes may cause a severe communication bottleneck. To overcome this challenge, over-the-air computing (AirComp) is a promising medium access technology, which exploits the superposition property of the wireless multiple access channel (MAC) and offers significant bandwidth savings. In this work, we propose an AirComp framework for general distributed convex optimization problems. Specifically, a distributed primal-dual (DPD) subgradient method is utilized for the optimization procedure. Under general assumptions, we prove that DPD-AirComp can asymptotically achieve zero expected constraint violation. Therefore, DPD-AirComp ensures the feasibility of the original problem, despite the presence of channel fading and additive noise. Moreover, with proper power control of the users’ signals, the expected non-zero optimality gap can also be mitigated. Two practical applications of the proposed framework are presented, namely, smart grid management and wireless resource allocation. Finally, numerical results confirm DPD-AirComp’s excellent performance, while it is also shown that DPD-AirComp converges an order of magnitude faster compared to two digital orthogonal multiple access schemes, specifically, time-division multiple access (TDMA), and orthogonal frequency-division multiple access (OFDMA).

A Second-Order Projected Primal-Dual Dynamical System for Distributed Optimization and Learning.

This article focuses on developing distributed optimization strategies for a class of machine learning problems over a directed network of computing agents. In these problems, the global objective function is an addition function, which is composed of local objective functions. Such local objective functions are convex and only endowed by the corresponding computing agent. A second-order Nesterov accelerated dynamical system with time-varying damping coefficient is developed to address such problems. To effectively deal with the constraints in the problems, the projected primal-dual method is carried out in the Nesterov accelerated system. By means of the cocoercive maximal monotone operator, it is shown that the trajectories of the Nesterov accelerated dynamical system can reach consensus at the optimal solution, provided that the damping coefficient and gains meet technical conditions. In the end, the validation of the theoretical results is demonstrated by the email classification problem and the logistic regression problem in machine learning.

Preconception contraceptive use and miscarriage: prospective cohort study

ObjectivesTo evaluate the association between preconception contraceptive use and miscarriage.DesignProspective cohort study.SettingResidents of the United States of America or Canada, recruited from 2013 until the end of 2022.Participants13 460 female...

Novel High-Precision and High-Robustness Localization Algorithm for Underwater-Environment-Monitoring Wireless Sensor Networks

In marine ecological environment monitoring, the acquisition of node location information is crucial, and the absence of location information can render the collected data meaningless. Compared to the rest of the distance-based localization methods, the received signal strength (RSS)-based localization technique has gained significant interest due to its low cost and the absence of time synchronization. However, the acoustic signal propagates in the complex and changeable aqueous medium, and, in addition to the time-varying path loss factor (PLF), there is often a certain absorption loss, which seriously deteriorates the localization accuracy of the RSS-based technique. To address the above challenges, we propose a novel high-precision and high-robustness localization (NHHL) algorithm that introduces an estimation parameter to conjointly estimate the marine node location and the ambient PLF. Firstly, the original non-convex localization problem is converted into an alternating nonnegative constrained least squares (ANCLS) framework with the unknown PLF and absorption loss, and a two-step localization method based on the primitive dual interior point method and block co-ordinate update method is presented to find the optimal solution. In the first step, the penalty function is utilized to reformulate the localization problem and find an approximate solution. Nevertheless, due to inherent errors, it is unable to approximate the constraint boundary and the global optimum solution. Subsequently, in the second step, the original localization problem is further transformed into a generalized trust region sub-problem (GTRS) framework, and the approximate solution of the interior point method is utilized as the initial estimation, and then iteratively solved by block co-ordinate update to obtain the precise location and PLF conjointly. Furthermore, the closed-form expression of the Cramér–Rao lower bound (CRLB) for the case of the unknown path loss factor and absorption loss is derived to evaluate the our NHHL algorithm. Finally, the simulation results demonstrate the superiority of the presented NHHL algorithm compared with the selected benchmark methods in various marine simulation scenarios.

REGULARIZED JACOBI-TYPE ADMM-METHOD FOR FINDING SOLUTIONS TO GENERALIZED NASH EQUILIBRIUM PROBLEM

In this paper, we extended the well-known alternating direction method of multipliers (ADMM) for optimization problems to generalized Nash equilibrium problems (GNEP) with shared constraints. We developed an ADMM-type algorithm with fixed regularization to tackle the problem (GNEP) where an upper estimate for the operator norm is not known and then we apply a multiplier-penalty in order to get rid of the joint constraints. We equipped the Hilbert space with an appropriate weighted scalar product and it turns out to be weakly convergent under a lipschitz and monotonicity assumption. A proximal term is then added to improve the convergence properties. Furthermore, a comparative analysis of quasi-variational inequality method, interior point method, penalty method and the proposed method are discussed.

Demographic Profile, Causes and Methods of Induced Abortion in a Tertiary Care Hospital, Dhaka, Bangladesh

Introduction: Induced abortions are those terminated by deliberate action undertaken to terminate a pregnancy. Information on the incidence of induced abortion is crucial for identifying policy and programmatic needs aimed at reducing unintended pregnancy. Because unsafe abortion is a cause of maternal morbidity and mortality, measures of its incidence are also important. This study aimed to analyze the sociodemographic characteristics of induced abortion. Methods: A descriptive cross-sectional study was conducted at the Department of Obstetrics and Gynaecology, Dhaka Medical College Hospital, Dhaka, Bangladesh. The sample was composed of 50 women who underwent induced abortion in this hospital, between January 2022 and January 2023. A simple random sampling technique was used in this study. Data were collected using a data collection sheet, processed, and analyzed by SPSS. version 22. Data were presented in tables and pie charts. The study was approved by the Ethics Committee of Dhaka Medical College Hospital. Informed written consent was taken from the respondents. Result: In this study, most of the patients (25, 50%) were in the 25-30 years age group, followed by (18, 36%) 31-35 years age group, and (7, 14%) the rest were in &gt;35 years age group, most people (30, 60%) resided in the urban areas and most of them (35, 70%) had a monthly income of &lt;15000 BDT, followed by (10, 20%) 15000-20000 BDT. Respondents were mostly (25, 50%) uneducated, some of them (15, 30%) passed secondary school, and (10, 20%) higher secondary school. Most of the patients (18, 36%) in this study used the barrier method for contraception, followed by (16, 32%) withdrawal method. Regarding the cause of induced abortion, unplanned pregnancy was the prominent cause (16, 32%), followed by, inadequate income (12, 24%), and contraception failure (12, 24%). Conclusion: This study concluded that most of the patients aged between 25 to 30 years and most of them resided in urban areas having a low monthly income, and poor education level. Some prominent causes of induced abortion were unplanned pregnancy, inadequate income, and contraceptive failure.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.