Paper Info
Title
Recognizing underlying sparsity in optimization
Abstract
Exploiting sparsity is essential to improve the efficiency of solving large optimization problems. We present a method for recognizing the underlying sparsity structure of a nonlinear partially separable problem, and show how the sparsity of the Hessian matrices of the problem’s functions can be improved by performing a nonsingular linear transformation in the space corresponding to the vector of variables. A combinatorial optimization problem is then formulated to increase the number of zeros of the Hessian matrices in the resulting transformed space, and a heuristic greedy algorithm is applied to this formulation. The resulting method can thus be viewed as a preprocessor for converting a problem with hidden sparsity into one in which sparsity is explicit. When it is combined with the sparse semidefinite programming relaxation by Waki et al. for polynomial optimization problems, the proposed method is shown to extend the performance and applicability of this relaxation technique. Preliminary numerical results are presented to illustrate this claim.
Year
DOI
Venue
2009
10.1007/s10107-008-0210-4
Math. Program.
Keywords
Field
DocType
combinatorial optimization problem,nonlinear optimization,separable problem,polynomial optimization problem,partial separability,hidden sparsity,polynomial optimization,hessian matrix,problem structure,sdp relaxation,exploiting sparsity,resulting method,large optimization problem,sparsity,underlying sparsity structure,greedy algorithm,linear transformation
Heuristic,Mathematical optimization,Nonlinear programming,Hessian matrix,Greedy algorithm,Combinatorial optimization,Optimization problem,Sparse matrix,Semidefinite programming,Mathematics
Journal
Volume
Issue
ISSN
119
2
1436-4646
Citations 
PageRank 
References 
6
0.47
12
Authors
3
Name
Order
Citations
PageRank
Sunyoung Kim146138.82
Masakazu Kojima21603222.51
Philippe L. Toint31397127.90