On Minimax Programming with Vanishing Constraints

In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ∊-subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.

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Necessary Stationary Conditions for Multiobjective Optimization Problems with Nondifferentiable Convex Vanishing Constraints

Iranian Journal of Science and Technology Transactions A Science ◽

10.1007/s40995-019-00768-4 ◽

2019 ◽

Vol 43 (6) ◽

pp. 2913-2919 ◽

Cited By ~ 1

Author(s):

J. Shaker Ardakani ◽

SH. Farahmand Rad ◽

N. Kanzi ◽

P. Reihani Ardabili

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Multiobjective Optimization Problems ◽

Vanishing Constraints ◽

Stationary Conditions

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A smoothing-regularization approach to mathematical programs with vanishing constraints

Computational Optimization and Applications ◽

10.1007/s10589-013-9539-6 ◽

2013 ◽

Vol 55 (3) ◽

pp. 733-767 ◽

Cited By ~ 18

Author(s):

Wolfgang Achtziger ◽

Tim Hoheisel ◽

Christian Kanzow

Keyword(s):

Mathematical Programs ◽

Vanishing Constraints

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An SQP method for mathematical programs with vanishing constraints with strong convergence properties

Computational Optimization and Applications ◽

10.1007/s10589-017-9894-9 ◽

2017 ◽

Vol 67 (2) ◽

pp. 361-399 ◽

Cited By ~ 2

Author(s):

Matúš Benko ◽

Helmut Gfrerer

Keyword(s):

Strong Convergence ◽

Convergence Properties ◽

Sqp Method ◽

Mathematical Programs ◽

Vanishing Constraints

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On Nonsmooth Semi-Infinite Minimax Programming Problem with(Φ,ρ)-Invexity

Abstract and Applied Analysis ◽

10.1155/2014/317304 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

X. L. Liu ◽

G. M. Lai ◽

C. Q. Xu ◽

D. H. Yuan

Keyword(s):

Optimality Conditions ◽

Programming Problem ◽

Necessary Optimality Conditions ◽

Duality Theorems ◽

Converse Duality ◽

Minimax Programming ◽

Carathéodory’S Theorem

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz(Φ,ρ)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.

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