Some Results about Duality and Exact Penalization

Authors:
Y. Y. Zhou;X. Q. Yang
Affiliations:
Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, China;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, P.R. China
Venue:
Journal of Global Optimization
Year:
2004

Citing 6
Cited 3

Lagrange multipliers and optimality

SIAM Review
Asymptotic analysis for penalty and barrier methods in convex and linear programming

Mathematics of Operations Research
A Nonlinear Lagrangian Approach to Constrained Optimization Problems

SIAM Journal on Optimization
Decreasing Functions with Applications to Penalization

SIAM Journal on Optimization
The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function

Mathematics of Operations Research
A Unified Augmented Lagrangian Approach to Duality and Exact Penalization

Mathematics of Operations Research

Augmented Lagrangian functions for constrained optimization problems

Journal of Global Optimization
Augmented Lagrangian function, non-quadratic growth condition and exact penalization

Operations Research Letters
Existence of augmented Lagrange multipliers for cone constrained optimization problems

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we introduce the concept of the valley at 0 augmenting function and apply it to construct a class of valley at 0 augmented Lagrangian functions. We establish the existence of a path of optimal solutions generated by valley at 0 augmented Lagrangian problems and its convergence toward the optimal set of the original problem and obtain the zero duality gap property between the primal problem and the valley at 0 augmented Lagrangian dual problem. Moreover, we establish the exact penalization representation results in the framework of valley at 0 augmented Lagrangian.