Paper Info
Title
A Geometrical Analysis on Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems
Abstract
We present a unified geometrical analysis on the completely positive programming (CPP) reformulations of quadratic optimization problems (QOPs) and their extension to polynomial optimization problems (POPs) based on a class of geometrically defined nonconvex conic programs and their convexification. The class of nonconvex conic programs minimize a linear objective function in a vector space V over the constraint set represented geometrically as the intersection of a nonconvex cone K subset of V, a face J of the convex hull of K, and a parallel translation L of a hyperplane. We show that under moderate assumptions, the original nonconvex conic program can equivalently be reformulated as a convex conic program by replacing the constraint set with the intersection of J and L. The replacement procedure is applied for deriving the CPP reformulations of QOPs and their extension to POPs.
Year
DOI
Venue
2020
10.1137/19M1237715
SIAM JOURNAL ON OPTIMIZATION
Keywords
DocType
Volume
completely positive programming reformulation,quadratic programs,polynomial optimization problems,conic optimization problems,faces of the completely positive cone
Journal
30
Issue
ISSN
Citations 
2
1052-6234
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
S. Kim124814.25
Masakazu Kojima21603222.51
Kim-Chuan Toh3109780.39