A nonlinear Lagrangian dual for integer programming

Authors:
Yifan Xu;Duan Li
Affiliations:
School of Management, Fudan University, Shanghai 200433, People's Republic of China;Department of System Engineering and Engineering Management, The Chinese University of Hong Kong, NT, Hong Kong
Venue:
Operations Research Letters
Year:
2002

Citing 10
Cited 2

Lagrangean decomposition: A model yielding stronger lagrangean bounds

Mathematical Programming: Series A and B
Lagrangian decomposition for integer nonlinear programming with linear constraints

Mathematical Programming: Series A and B
Lagrangean methods for 0-1 quadratic problems

Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
A primal dual integer programming algorithm

Discrete Applied Mathematics - ARIDAM IV and V
Zero duality gap for a class of nonconvex optimization problems

Journal of Optimization Theory and Applications
Local saddle points and convexification for nonconvex optimization problems

Journal of Optimization Theory and Applications
Value-estimation function method for constrained global optimization

Journal of Optimization Theory and Applications
Asymptotic Strong Duality for Bounded Integer Programming: A Logarithmic-Exponential Dual Formulation

Mathematics of Operations Research
Success Guarantee of Dual Search in Integer Programming: p-th Power Lagrangian Method

Journal of Global Optimization
Zero duality gap in integer programming: P-norm surrogate constraint method

Operations Research Letters

Generalized Nonlinear Lagrangian Formulation for Bounded Integer Programming

Journal of Global Optimization
Comment on "A nonlinear Lagrangian dual for integer programming"

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Nonlinear Lagrangian theory offers a success guarantee for the dual search via construction of a nonlinear support of the perturbation function at the optimal point. In this paper, a new nonlinear dual formulation of an exponential form is proposed for bounded integer programming. This new formulation possesses an asymptotic strong duality property and guarantees a success in identifying a primal optimum solution. No actual dual search is needed in the solution process when the parameter of the nonlinear Lagrangian formulation is set to be large enough.