Equivalence Relations in Convex Optimization

被引：0

作者：

Nurminski E.A. ^{[1
]}

机构：

[1] Far Eastern Federal University, Vladivostok

来源：

Journal of Applied and Industrial Mathematics | 2023年 / 17卷 / 02期

关键词：

convex optimization; projection; regularization; support function;

D O I：

10.1134/S1990478923020126

中图分类号：

O144 [集合论]; O157 [组合数学（组合学）];

学科分类号：

070104 ;

摘要：

Abstract: Several useful correspondences between general convex optimization problems, supportfunctions, and projection operations are established. These correspondences cover the asymptoticequivalence of projection operations and computation of support functions for general convex sets,hence the same equivalence for general convex optimization problems, and the equivalencebetween least-norm problems and the problem of regularized convex suplinear optimization. © 2023, Pleiades Publishing, Ltd.

引用

页码：339 / 344

页数：5

共 10 条

[1]

Nurminski E.A., Single-projection procedure for linear optimization, J. Glob. Optim., 66, 1, pp. 95-110, (2016)

[2]

Nurminski E.A., Projection onto polyhedra in outer representation, Comput. Math. Math. Phys., 48, 3, pp. 367-375, (2008)

[3]

Ablaev S.S., Makarenko D.V., Stonyakin F.S., Alkousa M.S., Baran I.V., Subgradient methods for non-smooth optimization problems with some relaxation of sharp minimum, Komp’yut. Issled. Model., 14, 2, pp. 473-495, (2022)

[4]

Bui Hoa T., Burachik R.S., Nurminski E.A., Tam M.K., Single-projection procedure for infinite dimensional convex optimization problems, E-Preprint

[5]

Nurminski E.A., Accelerating iterative methods for projection onto polyhedra, Far East. Math. Collect., 1, pp. 51-62, (1995)

[6]

Dolgopolik M.V., Exact penalty functions with multidimensional penalty parameter and adaptive penalty updates, Optim. Lett., 16, pp. 1281-1300, (2022)

[7]

Bauschke H.H., Borwein J.M., On projection algorithms for solving convex feasibility problems, SIAM Rev., 38, pp. 367-426, (1996)

[8]

Gould N.I.M., How good are projection methods for convex feasibility problems?, Comput. Optim. Appl., 40, pp. 1-12, (2008)

[9]

Censor Y., Chen W., Combettes P.L., Et al., On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Comput. Optim. Appl., 51, pp. 1065-1088, (2012)

[10]

Johnstone P.R., Eckstein J., Convergence rates for projective splitting, SIAM J. Optim., 29, 3, pp. 1931-1957, (2019)

← 1 →