Paper Info
Title
On global optimization with indefinite quadratics.
Abstract
We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them.
Year
DOI
Venue
2017
10.1007/s13675-016-0079-6
EURO J. Computational Optimization
Keywords
DocType
Volume
Global optimization, Indefinite quadratic, Difference of convex functions, Eigendecomposition, Semidefinite programming, Mixed-integer non-linear programming, 90-XX, 90Cxx, 90C26, 90C11, 90C20, 90C22
Journal
5
Issue
ISSN
Citations 
3
2192-4414
0
PageRank 
References 
Authors
0.34
12
3
Name
Order
Citations
PageRank
Marcia Fampa100.34
JON LEE27914.45
Wendel Melo3133.02