{"title":"Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems","authors":"","doi":"10.23952/asvao.5.2023.1.07","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.1.07","url":null,"abstract":"","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131608357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Connectedness properties of efficient and minimal sets to vector optimization problems","authors":"","doi":"10.23952/asvao.5.2023.1.08","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.1.08","url":null,"abstract":"","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115820941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimality conditions and duality relations in nonsmooth fractional interval-valued multiobjective optimization","authors":"N. Hung, N. Tuyen","doi":"10.23952/asvao.5.2023.1.03","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.1.03","url":null,"abstract":"This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions. Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions. Finally, a Mond--Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130037271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming","authors":"Hadi Abbaszadehpeivasti, E. Klerk, M. Zamani","doi":"10.23952/asvao.5.2023.2.02","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.2.02","url":null,"abstract":"In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation method. As a spin-off we provide a method to analyse the worst-case performance of the Gauss-Seidel iterative method for linear systems where the coefficient matrix is positive semidefinite with a positive diagonal.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123341981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stable-set and coloring bounds based on 0-1 quadratic optimization","authors":"Dunja Pucher, F. Rendl","doi":"10.23952/asvao.5.2023.2.08","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.2.08","url":null,"abstract":"We consider semidefinite relaxations of Stable-Set and Coloring, which are based on quadratic 0-1 optimization. Information about the stability number and the chromatic number is hidden in the objective function. This leads to simplified relaxations which depend mostly on the number of vertices of the graph. We also propose tightenings of the relaxations which are based on the maximal cliques of the underlying graph. Computational results on graphs from the literature show the strong potential of this new approach.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115350501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
{"title":"Projecting onto rectangular hyperbolic paraboloids in Hilbert space","authors":"Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang","doi":"10.23952/asvao.5.2023.2.04","DOIUrl":"https://doi.org/10.23952/asvao.5.2023.2.04","url":null,"abstract":"In $mathbb{R}^3$, a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic paraboloids in $mathbb{R}^n$. Motivated by his work, we provide a rigorous analysis of the associated projection. In some cases, finding this projection amounts to finding a certain root of a quintic or cubic polynomial. We also observe when the projection is not a singleton and point out connections to graphical and set convergence.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"29 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114103323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces","authors":"Anton Freund, U. Kohlenbach","doi":"10.23952/asvao.4.2022.3.06","DOIUrl":"https://doi.org/10.23952/asvao.4.2022.3.06","url":null,"abstract":"We analyze a proof of Bruck to obtain an explicit rate of asymptotic regularity for Ces`aro means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and a modulus η of uniform convexity. One ingredient for the proof by Bruck is a result of Pisier, which shows that every uniformly convex (in fact every uniformly nonsquare) Banach space has some Rademacher type q > 1 with a suitable constant C q . We explicitly determine q and C q , which only depend on the single value η (1) of our modulus. Beyond these specific results, we summarize how work of Bruck has inspired developments in the proof mining program, which applies tools from logic to obtain results in various areas of mathematics.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131459083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new view on risk measures associated with acceptance sets","authors":"M. Marohn, C. Tammer","doi":"10.23952/asvao.3.2021.3.09","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.3.09","url":null,"abstract":"In this paper, we study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial position of an institution is not acceptable, the decision maker has to raise new capital and invest it into a basket of so called eligible assets to change the current position such that the resulting one corresponds with an element of the acceptance set. Risk measures have been widely studied, see e.g. [17] for an overview. The risk measure that is considered here determines the minimal costs of making a financial position acceptable. In the literature, monetary risk measures are often defined as translation invariant functions and, thus, there is an equivalent formulation as GerstewitzFunctional (see Artzner et al. [2] and Jaschke, Küchler [29]). The Gerstewitz-Functional is an useful tool for separation and scalarization in multiobjective optimization in the non-convex case. In our paper, we study properties of the sublevel sets, strict sublevel sets and level lines of a risk measure defined on a linear space. Furthermore, we discuss the finiteness of the risk measure and relax the closedness assumptions. *Martin-Luther-University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Mathematics, 06099 Halle (Saale), Germany (E-mail: marcel.marohn@b-tu.de) Martin-Luther-University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Mathematics, 06099 Halle (Saale), Germany (E-mail: christiane.tammer@mathematik.uni-halle.de )","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124088703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Convergence theorems for a fixed point of $eta$-demimetric mappings in Banach spaces","authors":"N. Shahzad, H. Zegeye","doi":"10.23952/asvao.3.2021.2.04","DOIUrl":"https://doi.org/10.23952/asvao.3.2021.2.04","url":null,"abstract":"","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121464428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}