Optimization Letters最新文献

Newton-type algorithms for inverse optimization: weighted bottleneck Hamming distance and ℓ ∞ -norm objectives. 反优化的牛顿型算法：加权瓶颈汉明距离和l∞范数目标。

IF 1.1 4区数学

Optimization Letters Pub Date : 2025-01-01 Epub Date: 2025-01-21 DOI: 10.1007/s11590-024-02183-0

Kristóf Bérczi, Lydia Mirabel Mendoza-Cadena, Kitti Varga

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Newton-type algorithms for inverse optimization: weighted bottleneck Hamming distance and <ns0:math><ns0:msub><ns0:mi>ℓ</ns0:mi> <ns0:mi>∞</ns0:mi></ns0:msub> </ns0:math> -norm objectives.","authors":"Kristóf Bérczi, Lydia Mirabel Mendoza-Cadena, Kitti Varga","doi":"10.1007/s11590-024-02183-0","DOIUrl":"https://doi.org/10.1007/s11590-024-02183-0","url":null,"abstract":"In inverse optimization problems, we are given a feasible solution to an underlying optimization problem, and the goal is to modify the problem parameters so that the given input solution becomes optimal. In the minimum-cost setting, the underlying optimization problem is endowed with a linear cost function, and the goal is to modify the costs by a small deviation vector so that the input solution becomes optimal. The difference between the new and the original cost functions can be measured in several ways. In this paper, we focus on two objectives: the weighted bottleneck Hamming distance and the weighted <math><msub><mi>ℓ</mi> <mi>∞</mi></msub> </math> -norm. We consider a general model in which the coordinates of the deviation vector are required to fall within given lower and upper bounds. For the weighted bottleneck Hamming distance objective, we present a simple, purely combinatorial algorithm that determines an optimal deviation vector in strongly polynomial time. For the weighted <math><msub><mi>ℓ</mi> <mi>∞</mi></msub> </math> -norm objective, we give a min-max characterization for the optimal solution, and provide a pseudo-polynomial algorithm for finding an optimal deviation vector that runs in strongly polynomial time in the case of unit weights. For both objectives, we assume that an algorithm with the same time complexity for solving the underlying combinatorial optimization problem is available.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"19 8","pages":"1665-1690"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12532653/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145330675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A necessary condition for the guarantee of the superiorization method. 保证优化方法的必要条件。

IF 1.1 4区数学

Optimization Letters Pub Date : 2025-01-01 Epub Date: 2025-03-03 DOI: 10.1007/s11590-025-02192-7

Kay Barshad, Yair Censor, Walaa Moursi, Tyler Weames, Henry Wolkowicz

{"title":"A necessary condition for the guarantee of the superiorization method.","authors":"Kay Barshad, Yair Censor, Walaa Moursi, Tyler Weames, Henry Wolkowicz","doi":"10.1007/s11590-025-02192-7","DOIUrl":"10.1007/s11590-025-02192-7","url":null,"abstract":"We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization method (SM), where the iterates of an asymptotically convergent iterative feasibility-seeking algorithm are perturbed by objective function nonascent steps. We investigate the question under what conditions a sequence generated by an SM algorithm asymptotically converges to a feasible point whose objective function value is superior (meaning smaller or equal) to that of a feasible point reached by the corresponding unperturbed one (i.e., the exactly same feasibility-seeking algorithm that the SM algorithm employs.) This question is yet only partially answered in the literature. We present a condition under which an SM algorithm that uses negative gradient descent steps in its perturbations fails to yield such a superior outcome. The significance of the discovery of this \"negative condition\" is that it necessitates that the inverse of this condition will have to be assumed to hold in any future guarantee result for the SM. The condition is important for practitioners who use the SM because it is avoidable in experimental work with the SM, thus increasing the success rate of the method in real-world applications.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"19 8","pages":"1699-1714"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12532677/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145330642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Minimizing the number of tardy jobs with generalized due-dates and position-dependent processing times 最大限度地减少迟到工作的数量，同时采用通用的到期日和与位置相关的处理时间

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-09-13 DOI: 10.1007/s11590-024-02138-5

Enrique Gerstl, Gur Mosheiov