Convex optimization problems with arbitrary right-hand side perturbations

Abstract

The problem of finding a solution to a system of mixed variational inequalities, which can be interpreted as a generalization of a primal–dual formulation of an optimization problem under arbitrary right-hand side perturbations, is considered. A number of various equilibrium type problems are particular cases of this problem. We suggest the problem to be reduced to a class of variational inequalities and propose a general descent type method to find its solution. If the primal cost function does not possess strengthened convexity properties, this descent method can be combined with a partial regularization method.

Keywords:

• Optimization problems
• Arbitrary perturbations
• Dual descent method
• Equilibrium problems
• Mathematics Subject Classifications 2000: 90C30
• 65K10

Acknowledgement

The author is grateful to an anonymous referee for his/her valuable comments. This work was partially supported by RFBR Grant No. 04-01-00484.

Notes

E-mail: [email protected]

Additional information

Notes on contributors

I. V. Konnov *

E-mail: [email protected]