Journal of Optimization Theory and Applications最新文献_第6页

Bounds of the Solution Set to the Polynomial Complementarity Problem 多项式互补问题解集的边界

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-07-04 DOI: 10.1007/s10957-024-02484-5

Yang Xu, Guyan Ni, Mengshi Zhang

引用次数: 0

On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization 论多目标优化中点集的必要最优条件

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-07-03 DOI: 10.1007/s10957-024-02478-3

Andrea Cristofari, Marianna De Santis, Stefano Lucidi

{"title":"On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization","authors":"Andrea Cristofari, Marianna De Santis, Stefano Lucidi","doi":"10.1007/s10957-024-02478-3","DOIUrl":"https://doi.org/10.1007/s10957-024-02478-3","url":null,"abstract":"Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"48 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints 具有均衡约束条件的一类非 Lipschitz 数学程序的近似方法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-07-01 DOI: 10.1007/s10957-024-02475-6

Lei Guo, Gaoxi Li

{"title":"Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints","authors":"Lei Guo, Gaoxi Li","doi":"10.1007/s10957-024-02475-6","DOIUrl":"https://doi.org/10.1007/s10957-024-02475-6","url":null,"abstract":"We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz MPEC is highly challenging since the standard constraint qualifications fail due to the existence of equilibrium constraints and the subdifferential of the objective function is unbounded due to the existence of the non-Lipschitz function. On the one hand, for tackling the non-Lipschitzness of the objective function, we introduce a novel class of locally Lipschitz approximation functions that consolidate and unify a diverse range of existing smoothing techniques for the non-Lipschitz function. On the other hand, we use the Kanzow and Schwartz regularization scheme to approximate the equilibrium constraints since this regularization can preserve certain perpendicular structure as in equilibrium constraints, which can induce better convergence results. Then an approximation method is proposed for solving the non-Lipschitz MPEC and its convergence is established under weak conditions. In contrast with existing results, the proposed method can converge to a better stationary point under weaker qualification conditions. Finally, a computational study on the sparse solutions of linear complementarity problems is presented. The numerical results demonstrate the effectiveness of the proposed method.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"50 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches 依赖状态的扫频过程：渐近行为和算法方法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-07-01 DOI: 10.1007/s10957-024-02485-4

Samir Adly, Monica G. Cojocaru, Ba Khiet Le

引用次数: 0

Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds 黎曼曼曼体中准凸函数的近点法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-27 DOI: 10.1007/s10957-024-02482-7

Erik Alex Papa Quiroz

引用次数: 0

Primal–Dual Stability in Local Optimality 局部最优的原始-双重稳定性

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-24 DOI: 10.1007/s10957-024-02467-6

Matúš Benko, R. Tyrrell Rockafellar

引用次数: 0

The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems 多目标离散优化问题的加权 p 准则权集分解

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-24 DOI: 10.1007/s10957-024-02481-8

Stephan Helfrich, Kathrin Prinz, Stefan Ruzika

引用次数: 0

Efficient Use of Quantum Linear System Algorithms in Inexact Infeasible IPMs for Linear Optimization 在线性优化的不精确不可行 IPM 中有效利用量子线性系统算法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-23 DOI: 10.1007/s10957-024-02452-z

Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, Tamás Terlaky

{"title":"Efficient Use of Quantum Linear System Algorithms in Inexact Infeasible IPMs for Linear Optimization","authors":"Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, Tamás Terlaky","doi":"10.1007/s10957-024-02452-z","DOIUrl":"https://doi.org/10.1007/s10957-024-02452-z","url":null,"abstract":"Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially quantum interior point methods (QIPMs), to solve convex conic optimization problems. Most of them have applied a quantum linear system algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates in detail the use of quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point (II-QIPM) is developed to solve linear optimization problems. We also discuss how we can get an exact solution by iterative refinement (IR) without excessive time of quantum solvers. The proposed IR-II-QIPM shows exponential speed-up with respect to precision compared to previous II-QIPMs. Additionally, we present a quantum-inspired classical variant of the proposed IR-II-QIPM where QLSAs are replaced by conjugate gradient methods. This classic IR-II-IPM has some advantages compared to its quantum counterpart, as well as previous classic inexact infeasible IPMs. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are presented and analyzed.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Risk Evaluation and Control of Distributed Multi-agent Systems 论分布式多代理系统的风险评估与控制

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-21 DOI: 10.1007/s10957-024-02464-9

Aray Almen, Darinka Dentcheva

{"title":"On Risk Evaluation and Control of Distributed Multi-agent Systems","authors":"Aray Almen, Darinka Dentcheva","doi":"10.1007/s10957-024-02464-9","DOIUrl":"https://doi.org/10.1007/s10957-024-02464-9","url":null,"abstract":"In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive a dual representation for the systemic risk measures and propose new ways to construct families of systemic risk measures using either a collection of linear scalarizations or non-linear risk aggregation. The proposed framework facilitates risk-averse sequential decision-making by distributed methods. The new approach is compared theoretically and numerically to other systemic risk measurements from the existing literature. We formulate a two-stage decision problem for a distributed system using a systemic measure of risk. The structure accommodates distributed systems arising in energy networks, robotics, and other practical situations. A distributed decomposition method for solving the two-stage problem is proposed and applied to a problem arising in communication networks. We have used this problem to compare the methods of systemic risk evaluation. We show that the risk evaluation via linear scalarizations of outcomes leads to less conservative risk evaluation and results in a substantially better solution to the problem at hand than aggregating the risk of individual agents.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"14 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical Method for a Controlled Sweeping Process with Nonsmooth Sweeping Set 具有非光滑扫频集的受控扫频过程的数值方法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-06-19 DOI: 10.1007/s10957-024-02470-x

Chadi Nour, Vera Zeidan

引用次数: 0