Pub Date : 1900-01-01DOI: 10.23952/jano.2.2020.2.08
H. Yaohua, Yuping Liu, Li Minghua
. The quasi-convex feasibility problem (QFP), in which the involved functions are quasi-convex, is at the core of the modeling of many problems in various areas such as economics, finance and management science. In this paper, we consider an inexact incremental quasi-subgradient method to solve the QFP, in which an incremental control of component functions in the QFP is employed and the inex-actness stems from computation error and noise arising from practical considerations and physical cir-cumstances. Under the assumptions that the computation error and noise are deterministic and bounded and a H¨older condition on component functions in the QFP, we study the convergence property of the proposed inexact incremental quasi-subgradient method, and particularly, investigate the effect of the inexact terms on the incremental quasi-subgradient method when using the constant, diminishing and dynamic stepsize rules.
{"title":"The effect of deterministic noise on a quasi-subgradient method for quasi-convex feasibility problems","authors":"H. Yaohua, Yuping Liu, Li Minghua","doi":"10.23952/jano.2.2020.2.08","DOIUrl":"https://doi.org/10.23952/jano.2.2020.2.08","url":null,"abstract":". The quasi-convex feasibility problem (QFP), in which the involved functions are quasi-convex, is at the core of the modeling of many problems in various areas such as economics, finance and management science. In this paper, we consider an inexact incremental quasi-subgradient method to solve the QFP, in which an incremental control of component functions in the QFP is employed and the inex-actness stems from computation error and noise arising from practical considerations and physical cir-cumstances. Under the assumptions that the computation error and noise are deterministic and bounded and a H¨older condition on component functions in the QFP, we study the convergence property of the proposed inexact incremental quasi-subgradient method, and particularly, investigate the effect of the inexact terms on the incremental quasi-subgradient method when using the constant, diminishing and dynamic stepsize rules.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123096813","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 : 1900-01-01DOI: 10.23952/jano.3.2021.3.05
{"title":"On sequential optimality theorems for linear fractional optimization problems involving integral functions defined on $L_n^2 [0,1]$","authors":"","doi":"10.23952/jano.3.2021.3.05","DOIUrl":"https://doi.org/10.23952/jano.3.2021.3.05","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129691126","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 : 1900-01-01DOI: 10.23952/jano.4.2022.2.11
{"title":"Superiorization with a projected subgradient method","authors":"","doi":"10.23952/jano.4.2022.2.11","DOIUrl":"https://doi.org/10.23952/jano.4.2022.2.11","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128391000","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 : 1900-01-01DOI: 10.23952/jano.5.2023.1.06
Mohsine Jennane, E. Kalmoun, L. Lafhim
. In this paper, we establish optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ a surrogate problem and a suitable constraint qualification to state necessary M-stationary conditions in terms of Clarke sub-differentials. Moreover, we demonstrate that in different cases these M-stationary conditions becomes sufficient as well. Finally, we also present Weak and strong duality results of Wolfe an Mond-Weir types
{"title":"On nonsmooth multiobjective semi-infinite programming with switching constraints","authors":"Mohsine Jennane, E. Kalmoun, L. Lafhim","doi":"10.23952/jano.5.2023.1.06","DOIUrl":"https://doi.org/10.23952/jano.5.2023.1.06","url":null,"abstract":". In this paper, we establish optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ a surrogate problem and a suitable constraint qualification to state necessary M-stationary conditions in terms of Clarke sub-differentials. Moreover, we demonstrate that in different cases these M-stationary conditions becomes sufficient as well. Finally, we also present Weak and strong duality results of Wolfe an Mond-Weir types","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133988841","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 : 1900-01-01DOI: 10.23952/jano.2.2020.3.08
{"title":"A multi-view on the CQ algorithm for split feasibility problems: From optimization lens","authors":"","doi":"10.23952/jano.2.2020.3.08","DOIUrl":"https://doi.org/10.23952/jano.2.2020.3.08","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116523199","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 : 1900-01-01DOI: 10.23952/jano.2.2020.3.03
{"title":"$L^infty$-stability for a class of parametric optimal control problems with mixed pointwise constraints","authors":"","doi":"10.23952/jano.2.2020.3.03","DOIUrl":"https://doi.org/10.23952/jano.2.2020.3.03","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132267312","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 : 1900-01-01DOI: 10.23952/jano.2.2020.2.06
L. V. Nguyen, X. Qin
In this paper, we present some observations about variational analysis of minimal time functions. Some new results on generalized differentiation of directional minimal time functions are provided.
本文给出了关于极小时间函数的变分分析的一些观察结果。给出了方向性极小时间函数广义微分的一些新结果。
{"title":"On variational analysis for general distance functions","authors":"L. V. Nguyen, X. Qin","doi":"10.23952/jano.2.2020.2.06","DOIUrl":"https://doi.org/10.23952/jano.2.2020.2.06","url":null,"abstract":"In this paper, we present some observations about variational analysis of minimal time functions. Some new results on generalized differentiation of directional minimal time functions are provided.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132274408","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 : 1900-01-01DOI: 10.23952/jano.3.2021.1.05
{"title":"Minimax exactness and global saddle points of nonlinear augmented Lagrangians","authors":"","doi":"10.23952/jano.3.2021.1.05","DOIUrl":"https://doi.org/10.23952/jano.3.2021.1.05","url":null,"abstract":"","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134146910","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 : 1900-01-01DOI: 10.23952/jano.2.2020.1.01
T. Humphries, M. Loreto, B. Halter, W. O'Keeffe
In many mathematical formulations of significant real-world technological or physical problems, the objective function is exogenous to the modeling process which defines the constraints. In such cases, the faith of the modeler in the usefulness of an objective function for the application at hand is limited and it is probably not worthwhile to invest a great effort in reaching an exact constrained minimum point. This is a major justification for using the superiorization method for practical applications.
{"title":"A special issue focused on superiorization versus constrained optimization: analysis and applications","authors":"T. Humphries, M. Loreto, B. Halter, W. O'Keeffe","doi":"10.23952/jano.2.2020.1.01","DOIUrl":"https://doi.org/10.23952/jano.2.2020.1.01","url":null,"abstract":"In many mathematical formulations of significant real-world technological or physical problems, the objective function is exogenous to the modeling process which defines the constraints. In such cases, the faith of the modeler in the usefulness of an objective function for the application at hand is limited and it is probably not worthwhile to invest a great effort in reaching an exact constrained minimum point. This is a major justification for using the superiorization method for practical applications.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124049078","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 : 1900-01-01DOI: 10.23952/jano.2.2020.2.03
WU Can, Yunhai Xiao, Li Peili
. Estimating a large and sparse inverse covariance matrix is a fundamental problem in modern multivariate analysis. Recently, a generalized model for a sparse estimation was proposed in which an explicit eigenvalue bounded constraint is involved. It covers a large number of existing estimation approaches as special cases. It was shown that the dual of the generalized model contains five separable blocks, which cause more challenges for minimizing. In this paper, we use an augmented Lagrangian method to solve the dual problem, but we minimize the augmented Lagrangian function with respect to each variable in a Jacobian manner, and add a proximal point term to make each subproblem easy to solve. We show that this iterative scheme is equivalent to adding a proximal point term to the augmented Lagrangian function, and its convergence can be directly followed. Finally, we give numerical simulations by using the synthetic data which show that the proposed algorithm is very effective in estimating high-dimensional sparse inverse covariance matrices.
{"title":"Semi-proximal augmented Lagrangian method for sparse estimation of high-dimensional inverse covariance matrices","authors":"WU Can, Yunhai Xiao, Li Peili","doi":"10.23952/jano.2.2020.2.03","DOIUrl":"https://doi.org/10.23952/jano.2.2020.2.03","url":null,"abstract":". Estimating a large and sparse inverse covariance matrix is a fundamental problem in modern multivariate analysis. Recently, a generalized model for a sparse estimation was proposed in which an explicit eigenvalue bounded constraint is involved. It covers a large number of existing estimation approaches as special cases. It was shown that the dual of the generalized model contains five separable blocks, which cause more challenges for minimizing. In this paper, we use an augmented Lagrangian method to solve the dual problem, but we minimize the augmented Lagrangian function with respect to each variable in a Jacobian manner, and add a proximal point term to make each subproblem easy to solve. We show that this iterative scheme is equivalent to adding a proximal point term to the augmented Lagrangian function, and its convergence can be directly followed. Finally, we give numerical simulations by using the synthetic data which show that the proposed algorithm is very effective in estimating high-dimensional sparse inverse covariance matrices.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124146105","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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