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Computing the Minimum-Time Interception of a Moving Target 计算拦截移动目标的最短时间
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-07-06 DOI: 10.1007/s10957-024-02487-2
Maksim Buzikov
{"title":"Computing the Minimum-Time Interception of a Moving Target","authors":"Maksim Buzikov","doi":"10.1007/s10957-024-02487-2","DOIUrl":"https://doi.org/10.1007/s10957-024-02487-2","url":null,"abstract":"<p>In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a moving target whose trajectory is known a priori. Our framework employs an analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without losing the guarantee of its convergence to the correct solution for arbitrary Lipschitz continuous trajectories of the moving target. In practice, it is difficult to obtain an analytical description of the distance to the reachable set for the sophisticated state equation of the plant. Nevertheless, it was shown that the distance can be obtained for some widely used models, such as the Dubins car, in an explicit form. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and the Dubins model.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"40 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572971","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
A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$mathbb {R}^{3}$$ 在 $$mathbb {R}^{3}$ 中对参数化曲面进行全局优化的新贝叶斯方法
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-07-06 DOI: 10.1007/s10957-024-02473-8
Anis Fradi, Chafik Samir, Ines Adouani
{"title":"A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$mathbb {R}^{3}$$","authors":"Anis Fradi, Chafik Samir, Ines Adouani","doi":"10.1007/s10957-024-02473-8","DOIUrl":"https://doi.org/10.1007/s10957-024-02473-8","url":null,"abstract":"<p>This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence and the uniqueness of a global solution. We also propose a new Bayesian clustering approach where local distributions of surfaces are modeled with spherical Gaussian processes. The maximization of the posterior density is performed with Hamiltonian dynamics which provide a natural and computationally efficient spherical Hamiltonian Monte Carlo sampling. Experimental results demonstrate the efficiency of the proposed method.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572972","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
Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition 凸预测器-非凸校正器优化策略在信号分解中的应用
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-07-04 DOI: 10.1007/s10957-024-02479-2
Laura Girometti, Martin Huska, Alessandro Lanza, Serena Morigi
{"title":"Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition","authors":"Laura Girometti, Martin Huska, Alessandro Lanza, Serena Morigi","doi":"10.1007/s10957-024-02479-2","DOIUrl":"https://doi.org/10.1007/s10957-024-02479-2","url":null,"abstract":"<p>Many tasks in real life scenarios can be naturally formulated as nonconvex optimization problems. Unfortunately, to date, the iterative numerical methods to find even only the local minima of these nonconvex cost functions are extremely slow and strongly affected by the initialization chosen. We devise a predictor–corrector strategy that efficiently computes locally optimal solutions to these problems. An initialization-free convex minimization allows to <i>predict</i> a global good preliminary candidate, which is then <i>corrected</i> by solving a parameter-free nonconvex minimization. A simple algorithm, such as alternating direction method of multipliers works surprisingly well in producing good solutions. This strategy is applied to the challenging problem of decomposing a 1D signal into semantically distinct components mathematically identified by smooth, piecewise-constant, oscillatory structured and unstructured (noise) parts.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549444","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
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
{"title":"Bounds of the Solution Set to the Polynomial Complementarity Problem","authors":"Yang Xu, Guyan Ni, Mengshi Zhang","doi":"10.1007/s10957-024-02484-5","DOIUrl":"https://doi.org/10.1007/s10957-024-02484-5","url":null,"abstract":"<p>In this paper, we investigate bounds of solution set of the polynomial complementarity problem. When a polynomial complementarity problem has a solution, we propose a lower bound of solution norm by entries of coefficient tensors of the polynomial. We prove that the proposing lower bound is larger than some existing lower bounds appeared in tensor complementarity problems and polynomial complementarity problems. When the solution set of a polynomial complementarity problem is nonempty, and the coefficient tensor of the leading term of the polynomial is an <span>(R_0)</span>-tensor, we propose a new upper bound of solution norm of the polynomial complementarity problem by a quantity defining by an optimization problem. Furthermore, we prove that when coefficient tensors of the polynomial are partially symmetric, the proposing lower bound formula with respect to tensor tuples reaches the maximum value, and the proposing upper bound formula with respect to tensor tuples reaches the minimum value. Finally, by using such partial symmetry, we obtain bounds of solution norm by coefficients of the polynomial.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"41 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549446","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 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":"<p>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.</p>","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":"<p>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.</p>","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
{"title":"State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches","authors":"Samir Adly, Monica G. Cojocaru, Ba Khiet Le","doi":"10.1007/s10957-024-02485-4","DOIUrl":"https://doi.org/10.1007/s10957-024-02485-4","url":null,"abstract":"<p>In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"30 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526728","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
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
{"title":"Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds","authors":"Erik Alex Papa Quiroz","doi":"10.1007/s10957-024-02482-7","DOIUrl":"https://doi.org/10.1007/s10957-024-02482-7","url":null,"abstract":"<p>This paper studies the convergence of the proximal point method for quasiconvex functions in finite dimensional complete Riemannian manifolds. We prove initially that, in the general case, when the objective function is proper and lower semicontinuous, each accumulation point of the sequence generated by the method, if it exists, is a limiting critical point of the function. Then, under the assumptions that the sectional curvature of the manifold is bounded above by some non negative constant and the objective function is quasiconvex we analyze two cases. When the constant is zero, the global convergence of the algorithm to a limiting critical point is assured and if it is positive, we prove the local convergence for a class of quasiconvex functions, which includes Lipschitz functions.\u0000</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502009","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
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
{"title":"Primal–Dual Stability in Local Optimality","authors":"Matúš Benko, R. Tyrrell Rockafellar","doi":"10.1007/s10957-024-02467-6","DOIUrl":"https://doi.org/10.1007/s10957-024-02467-6","url":null,"abstract":"<p>Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem’s parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multiplier vector associated with it exhibit that dependence as a primal–dual pair. In classical nonlinear programming, such advantageous behavior is tied to the combination of the standard strong second-order sufficient condition (SSOC) for local optimality and the linear independent gradient condition (LIGC) on the active constraint gradients. But although second-order sufficient conditons have successfully been extended far beyond nonlinear programming, insights into what should replace constraint gradient independence as the extended dual counterpart have been lacking. The exact answer is provided here for a wide range of optimization problems in finite dimensions. Behind it are advances in how coderivatives and strict graphical derivatives can be deployed. New results about strong metric regularity in solving variational inequalities and generalized equations are obtained from that as well.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"17 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502011","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 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
{"title":"The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems","authors":"Stephan Helfrich, Kathrin Prinz, Stefan Ruzika","doi":"10.1007/s10957-024-02481-8","DOIUrl":"https://doi.org/10.1007/s10957-024-02481-8","url":null,"abstract":"<p>Many solution algorithms for multiobjective optimization problems are based on scalarization methods that transform the multiobjective problem into a scalar-valued optimization problem. In this article, we study the theory of weighted <span>(p)</span>-norm scalarizations. These methods minimize the distance induced by a weighted <span>(p)</span>-norm between the image of a feasible solution and a given reference point. We provide a comprehensive theory of the set of eligible weights and, in particular, analyze the topological structure of the normalized weight set. This set is composed of connected subsets, called weight set components which are in a one-to-one relation with the set of optimal images of the corresponding weighted <span>(p)</span>-norm scalarization. Our work generalizes and complements existing results for the weighted sum and the weighted Tchebycheff scalarization and provides new insights into the structure of the set of all Pareto optimal solutions.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502010","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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