Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.03
{"title":"Existence and stability to vector optimization problems via improvement sets","authors":"","doi":"10.23952/jano.5.2023.2.03","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.03","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"195 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124340316","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}
Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.07
{"title":"A note on the subdifferential of convex multi-composite functionals","authors":"","doi":"10.23952/jano.5.2023.2.07","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.07","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134569198","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}
Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.01
{"title":"Multi-step actor-critic framework for reinforcement learning in continuous control","authors":"","doi":"10.23952/jano.5.2023.2.01","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.01","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122119522","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}
Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.02
Jiao Teng, DU Xian, Lei Wang, Xinwei Wang, Junmei Wu
. In this paper, we consider optimal control problems with linear discrete state space model, which originate from a class of turbofan engines. The optimization problem associated with each moving horizon estimation (MHE) in classical model predictive control (MPC) is a quadratic programming (QP) problem, and the general QP algorithms does not exploit the structural features of the turbofan engine itself to improve the computational efficiency of the algorithm. In the framework of model predictive control, the turbofan engine model makes the rolling optimization subproblem exhibit a sparse structure. Based on this feature, the alternating direction method of multipliers (ADMM) is employed to solve each optimization sub-problem and design an improved MPC-ADMM algorithm for solving this class of optimal control problems. The simulation results are compared with the MPC-QP algorithm by numerical examples to show the effectiveness and superiority of the novel algorithm.
{"title":"Model predictive control of discrete-time linear systems by ADMM with applications to turbofan engine control problems","authors":"Jiao Teng, DU Xian, Lei Wang, Xinwei Wang, Junmei Wu","doi":"10.23952/jano.5.2023.2.02","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.02","url":null,"abstract":". In this paper, we consider optimal control problems with linear discrete state space model, which originate from a class of turbofan engines. The optimization problem associated with each moving horizon estimation (MHE) in classical model predictive control (MPC) is a quadratic programming (QP) problem, and the general QP algorithms does not exploit the structural features of the turbofan engine itself to improve the computational efficiency of the algorithm. In the framework of model predictive control, the turbofan engine model makes the rolling optimization subproblem exhibit a sparse structure. Based on this feature, the alternating direction method of multipliers (ADMM) is employed to solve each optimization sub-problem and design an improved MPC-ADMM algorithm for solving this class of optimal control problems. The simulation results are compared with the MPC-QP algorithm by numerical examples to show the effectiveness and superiority of the novel algorithm.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128648114","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}
Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.06
{"title":"Iterative solutions of split fixed point and monotone inclusion problems in Hilbert spaces","authors":"","doi":"10.23952/jano.5.2023.2.06","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.06","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121612699","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}
Pub Date : 2023-08-01DOI: 10.23952/jano.5.2023.2.04
{"title":"IdentifyMix: An efficient two-stage learning approach to combating label noise","authors":"","doi":"10.23952/jano.5.2023.2.04","DOIUrl":"https://doi.org/10.23952/jano.5.2023.2.04","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"268 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132642335","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}
Pub Date : 2022-12-05DOI: 10.23952/jano.5.2023.1.12
J. E. Mart'inez-Legaz
Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and cyclically monotone. This paper presents an alternative characterization, which does not involve cyclic monotonicity. In the case of subdifferential operators of sublinear functions, the new characterization substantially simplifies. Dually, the new characterization of normal cone operators is very simple, too.
{"title":"Fenchel subdifferential operators: A characterization without cyclic monotonicity","authors":"J. E. Mart'inez-Legaz","doi":"10.23952/jano.5.2023.1.12","DOIUrl":"https://doi.org/10.23952/jano.5.2023.1.12","url":null,"abstract":"Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and cyclically monotone. This paper presents an alternative characterization, which does not involve cyclic monotonicity. In the case of subdifferential operators of sublinear functions, the new characterization substantially simplifies. Dually, the new characterization of normal cone operators is very simple, too.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116849559","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}
Pub Date : 2022-05-19DOI: 10.23952/jano.5.2023.1.09
C. Zălinescu
Lemma 1 from the paper [N.E. Gretsky, J.M. Ostroy, W.R. Zame, Subdifferentiability and the duality gap, Positivity 6: 261–274, 2002] asserts that the value function v of an infinite dimensional linear programming problem in standard form is lower semicontinuous whenever v is proper and the involved spaces are normed vector spaces. In this note one shows that this statement is false even in finite-dimensional spaces, one provides an example of linear programming problem in Hilbert spaces whose (proper) value function is not lower semicontinuous (hence it is not subdifferentiable) at any point in its domain, one shows that the restriction of the value function to its domain in Kretschmer’s gap example is not bounded on any neighborhood of any point of the domain, and discuss other assertions done in the same paper.
{"title":"On the lower semicontinuity and subdifferentiability of the value function for conic linear programming problems","authors":"C. Zălinescu","doi":"10.23952/jano.5.2023.1.09","DOIUrl":"https://doi.org/10.23952/jano.5.2023.1.09","url":null,"abstract":"Lemma 1 from the paper [N.E. Gretsky, J.M. Ostroy, W.R. Zame, Subdifferentiability and the duality gap, Positivity 6: 261–274, 2002] asserts that the value function v of an infinite dimensional linear programming problem in standard form is lower semicontinuous whenever v is proper and the involved spaces are normed vector spaces. In this note one shows that this statement is false even in finite-dimensional spaces, one provides an example of linear programming problem in Hilbert spaces whose (proper) value function is not lower semicontinuous (hence it is not subdifferentiable) at any point in its domain, one shows that the restriction of the value function to its domain in Kretschmer’s gap example is not bounded on any neighborhood of any point of the domain, and discuss other assertions done in the same paper.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123881955","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}
Pub Date : 2022-01-02DOI: 10.23952/jano.5.2023.1.08
Jinlu Li
In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1. In general, the conditions for a topological vector space to be quasi-pointseparable is not very difficult to check; 2. The class of quasi-point-separable topological vector spaces is very large that includes locally convex topological vector spaces and pseudonorm adjoint topological vector spaces as special cases; 3. Every quasi-point-separable Housdorrf topological vector space has the fixed point property (that is, every continuous self-mapping on any given nonempty closed and convex subset has a fixed point), which is the result of the main theorem of this paper (Theorem 4.1); Furthermore, we provide some concrete examples of quasi-point-separable topological vector spaces, which are not locally convex. It follows that the main theorem of this paper is a proper extension of Tychonoff’s fixed point theorem on locally convex topological vector spaces.
{"title":"The fixed point property of quasi-point-separable topological vector spaces","authors":"Jinlu Li","doi":"10.23952/jano.5.2023.1.08","DOIUrl":"https://doi.org/10.23952/jano.5.2023.1.08","url":null,"abstract":"In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1. In general, the conditions for a topological vector space to be quasi-pointseparable is not very difficult to check; 2. The class of quasi-point-separable topological vector spaces is very large that includes locally convex topological vector spaces and pseudonorm adjoint topological vector spaces as special cases; 3. Every quasi-point-separable Housdorrf topological vector space has the fixed point property (that is, every continuous self-mapping on any given nonempty closed and convex subset has a fixed point), which is the result of the main theorem of this paper (Theorem 4.1); Furthermore, we provide some concrete examples of quasi-point-separable topological vector spaces, which are not locally convex. It follows that the main theorem of this paper is a proper extension of Tychonoff’s fixed point theorem on locally convex topological vector spaces.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123755284","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}
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