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On the Uniform Duality in Copositive Optimization 论共正优化中的均匀对偶性
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-29 DOI: 10.1007/s10957-024-02515-1
O. I. Kostyukova, T. V. Tchemisova, O. S. Dudina
{"title":"On the Uniform Duality in Copositive Optimization","authors":"O. I. Kostyukova, T. V. Tchemisova, O. S. Dudina","doi":"10.1007/s10957-024-02515-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02515-1","url":null,"abstract":"<p>In this paper, we establish new necessary and sufficient conditions guaranteeing the uniform LP duality for linear problems of Copositive Programming and formulate these conditions in different equivalent forms. The main results are obtained using the approach developed in previous papers of the authors and based on a concept of immobile indices that permits alternative representations of the set of feasible solutions.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"23 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186664","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
Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications 局部重现性下的变分和准变分不等式：求解概念与应用
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-28 DOI: 10.1007/s10957-024-02493-4
Didier Aussel, Parin Chaipunya
{"title":"Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications","authors":"Didier Aussel, Parin Chaipunya","doi":"10.1007/s10957-024-02493-4","DOIUrl":"https://doi.org/10.1007/s10957-024-02493-4","url":null,"abstract":"<p>Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in lack of convexity or else when available numerical techniques are too limited for global solutions. Nevertheless, the analysis of such problems found in the literature seems to be very restricted to the global treatment. Motivated by this fact, in this work, we propose local solution concepts, study their interrelations and relations with global concepts and prove existence results as well as stability of local solution map of parametric variational inequalities. The key ingredient of our results is the new concept of local reproducibility of a set-valued map, which we introduce to explore such local solutions to quasi-variational inequality problems. As a by-product, we obtain local solutions to quasi-optimization problems, bilevel quasi-optimization problems and Single-Leader-Multi-Follower games.\u0000</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"10 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186666","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
Optimal Control Problem with Regular Mixed Constraints via Penalty Functions 通过惩罚函数解决具有常规混合约束条件的最优控制问题
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-28 DOI: 10.1007/s10957-024-02510-6
Maria do Rosário de Pinho, Maria Margarida A. Ferreira, Georgi Smirnov
{"title":"Optimal Control Problem with Regular Mixed Constraints via Penalty Functions","authors":"Maria do Rosário de Pinho, Maria Margarida A. Ferreira, Georgi Smirnov","doi":"10.1007/s10957-024-02510-6","DOIUrl":"https://doi.org/10.1007/s10957-024-02510-6","url":null,"abstract":"<p>Below we derive necessary conditions of optimality for problems with mixed constraints (see Dmitruk in Control Cybern 38(4A):923–957, 2009) using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., De Pinho et al. in Optimization 71(11):3363–3381, 2022) and, more recently, to solve optimal control problems with pure state constraints (see De Pinho et al. in Syst Control Lett 188:105816, 2024). We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact. Based on our penalty functions approach we develop a numerical method admitting estimates for its parameters needed to achieve a given precision.\u0000</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186665","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
Approximate Controllability of Abstract Discrete Fractional Systems of Order $$1 通过残差序列实现阶数 $$1<alpha <2$$ 的抽象离散分式系统的近似可控性
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-28 DOI: 10.1007/s10957-024-02516-0
Rodrigo Ponce
{"title":"Approximate Controllability of Abstract Discrete Fractional Systems of Order $$1<alpha <2$$ via Resolvent Sequences","authors":"Rodrigo Ponce","doi":"10.1007/s10957-024-02516-0","DOIUrl":"https://doi.org/10.1007/s10957-024-02516-0","url":null,"abstract":"<p>We study the approximate controllability of the discrete fractional systems of order <span>(1&lt;alpha &lt;2)</span></p><span>$$begin{aligned} (*)quad ,_Cnabla ^{alpha } u^n=Au^n+Bv^n+f(n,u^n), quad nge 2, end{aligned}$$</span><p>subject to the initial states <span>(u^0=x_0,u^1=x_1,)</span> where <i>A</i> is a closed linear operator defined in a Hilbert space <i>X</i>, <i>B</i> is a bounded linear operator from a Hilbert space <i>U</i> into <span>(X, f:{mathbb {N}}_0times Xrightarrow X)</span> is a given sequence and <span>(,_Cnabla ^{alpha } u^n)</span> is an approximation of the Caputo fractional derivative <span>(partial ^alpha _t)</span> of <i>u</i> at <span>(t_n:=tau n,)</span> where <span>(tau &gt;0)</span> is a given step size. To do this, we first study resolvent sequences <span>({S_{alpha ,beta }^n}_{nin {mathbb {N}}_0})</span> generated by closed linear operators to obtain some subordination results. In addition, we discuss the existence of solutions to <span>((*))</span> and next, we study the existence of optimal controls to obtain the approximate controllability of the discrete fractional system <span>((*))</span> in terms of the resolvent sequence <span>({S_{alpha ,beta }^n}_{nin {mathbb {N}}_0})</span> for some <span>(alpha ,beta &gt;0.)</span> Finally, we provide an example to illustrate our results.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186764","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
An Adaptive Distributionally Robust Optimization Approach for Optimal Sizing of Hybrid Renewable Energy Systems 自适应分布式鲁棒性优化方法，用于优化混合可再生能源系统的选型
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-26 DOI: 10.1007/s10957-024-02518-y
Ali Keyvandarian, Ahmed Saif
{"title":"An Adaptive Distributionally Robust Optimization Approach for Optimal Sizing of Hybrid Renewable Energy Systems","authors":"Ali Keyvandarian, Ahmed Saif","doi":"10.1007/s10957-024-02518-y","DOIUrl":"https://doi.org/10.1007/s10957-024-02518-y","url":null,"abstract":"<p>Hybrid renewable energy systems (HRESs) that integrate conventional and renewable energy generation and energy storage technologies represent a viable option to serve the energy demand of remote and isolated communities. A common way to capture the stochastic nature of demand and renewable energy supply in such systems is by using a small number of independent discrete scenarios. However, some information is inevitably lost when extracting these scenarios from historical data, thus introducing errors and biases to the design process. This paper proposes two frameworks, namely <i>robust-stochastic optimization</i> and <i>distributionally robust optimization</i>, that aim to hedge against the resulting uncertainty of scenario characterization and probability, respectively, in scenario-based HRES design approaches. Mathematical formulations are provided for the nominal, stochastic, robust-stochastic, distributional robust, and combined problems, and directly-solvable tractable reformulations are derived for the stochastic and the distributional robust cases. Furthermore, an exact column-and-constraint-generation algorithm is developed for the robust-stochastic and combined cases. Numerical results obtained from a realistic case study of a stand-alone solar-wind-battery-diesel HRES serving a small community in Northern Ontario, Canada reveal the performance advantage, in terms of both cost and utilization of renewable sources, of the proposed frameworks compared to classical deterministic and stochastic models, and their ability to mitigate the issue of information loss due to scenario reduction.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186668","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
Integral Resolvent and Proximal Mixtures 积分溶剂和近端混合物
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-24 DOI: 10.1007/s10957-024-02466-7
Minh N. Bùi, Patrick L. Combettes
{"title":"Integral Resolvent and Proximal Mixtures","authors":"Minh N. Bùi, Patrick L. Combettes","doi":"10.1007/s10957-024-02466-7","DOIUrl":"https://doi.org/10.1007/s10957-024-02466-7","url":null,"abstract":"<p>Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear operators. As a special case, we investigate the resolvent expectation, an operation which combines monotone operators in such a way that the resulting resolvent is the Lebesgue expectation of the individual resolvents. Along the same lines, we introduce an operation that mixes arbitrary families of convex functions defined on different spaces and linear operators to create a composite convex function. Such constructs have so far been limited to finite families of operators and functions. The subdifferential of the integral proximal mixture is shown to be the integral resolvent mixture of the individual subdifferentials. Applications to the relaxation of systems of composite monotone inclusions are presented.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186669","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
The Bounds of Solutions to Polynomial Complementarity Problems 多项式互补问题解的边界
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-23 DOI: 10.1007/s10957-024-02511-5
Xue-liu Li, Guo-ji Tang
{"title":"The Bounds of Solutions to Polynomial Complementarity Problems","authors":"Xue-liu Li, Guo-ji Tang","doi":"10.1007/s10957-024-02511-5","DOIUrl":"https://doi.org/10.1007/s10957-024-02511-5","url":null,"abstract":"<p>The polynomial complementarity problem (PCP) is an important extension of the tensor complementarity problem (TCP). The main purpose of the present paper is to extend the results on the bounds of solutions of TCP due to Xu–Gu–Huang from TCP to PCP. To that end, the concepts of (generalized) row strictly diagonally dominant tensor to tensor tuple are extended and the properties about them are discussed. By using the introduced structured tensor tuples, the upper and lower bounds on the norm of solutions to PCP are derived. Comparisons between the results presented in the present paper and the existing bounds are made.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"46 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186670","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
Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds 黎曼形状芒模中的随机增量拉格朗日法
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-21 DOI: 10.1007/s10957-024-02488-1
Caroline Geiersbach, Tim Suchan, Kathrin Welker
{"title":"Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds","authors":"Caroline Geiersbach, Tim Suchan, Kathrin Welker","doi":"10.1007/s10957-024-02488-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02488-1","url":null,"abstract":"<p>In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"159 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186671","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
Regularized and Structured Tensor Total Least Squares Methods with Applications 正规化和结构化张量最小二乘法及其应用
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-12 DOI: 10.1007/s10957-024-02507-1
Feiyang Han, Yimin Wei, Pengpeng Xie
{"title":"Regularized and Structured Tensor Total Least Squares Methods with Applications","authors":"Feiyang Han, Yimin Wei, Pengpeng Xie","doi":"10.1007/s10957-024-02507-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02507-1","url":null,"abstract":"<p>Total least squares (TLS), also named as errors in variables in statistical analysis, is an effective method for solving linear equations with the situations, when noise is not just in observation data but also in mapping operations. Besides, the Tikhonov regularization is widely considered in plenty of ill-posed problems. Moreover, the structure of mapping operator plays a crucial role in solving the TLS problem. Tensor operators have some advantages over the characterization of models, which requires us to build the corresponding theory on the tensor TLS. This paper proposes tensor regularized TLS and structured tensor TLS methods for solving ill-conditioned and structured tensor equations, respectively, adopting a tensor-tensor-product. Properties and algorithms for the solution of these approaches are also presented and proved. Based on this method, some applications in image and video deblurring are explored. Numerical examples illustrate the effectiveness of our methods, compared with some existing methods.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"2 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186672","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
Continuous Equality Knapsack with Probit-Style Objectives 带有 Probit 类型目标的连续等价包
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-08-12 DOI: 10.1007/s10957-024-02503-5
Jamie Fravel, Robert Hildebrand, Laurel Travis
{"title":"Continuous Equality Knapsack with Probit-Style Objectives","authors":"Jamie Fravel, Robert Hildebrand, Laurel Travis","doi":"10.1007/s10957-024-02503-5","DOIUrl":"https://doi.org/10.1007/s10957-024-02503-5","url":null,"abstract":"<p>We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"160 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935095","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
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