Smoothing method for minimizing the sum of the r largest functions

Authors:
Shaohua Pan;Suyan He;Xingsi Li
Affiliations:
Department of Applied Mathematics, South China University of Technology, Guangzhou, P.R. China;Software College of Dalian University of Foreign Languages, Dalian High-Tech Zone, Dalian, P.R. China;State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, China
Venue:
Optimization Methods & Software
Year:
2007

Citing 11
Cited 0

On the limited memory BFGS method for large scale optimization

Mathematical Programming: Series A and B
A smoothing technique for nondifferentiable optimization problems

Proceedings of the international seminar on Optimization
Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Smoothing methods for convex inequalities and linear complementarity problems

Mathematical Programming: Series A and B
Determinant Maximization with Linear Matrix Inequality Constraints

SIAM Journal on Matrix Analysis and Applications
Linear Programming in Linear Time When the Dimension Is Fixed

Journal of the ACM (JACM)
The k-centrum multi-faculty location problem

Discrete Applied Mathematics
Minimax parametric optimization problems and multi-dimensional parametric searching

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Minimizing the sum of the k largest functions in linear time

Information Processing Letters
Efficient Algorithms for the Smallest Enclosing Ball Problem

Computational Optimization and Applications
Faster minimization of linear wirelength for global placement

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a collection [image omitted] of m functions defined on Ren, we consider the problem of minimizing the sum of the r largest functions of the collection. This problem has significant applications in the science of facility location. In this article, we reformulate this problem as a nonsmooth problem only involving the maximum function max{0, t} and then develop a globally convergent smoothing method for the case that all of gi (x) are convex functions. This method is specifically applied to the collection of Euclidean distance functions defined by location models. Our computational experiments and numerical comparisons with the successful SeDuMi software indicate that the method is very promising and is able to solve problems of dimension n up to 10,000 efficiently.