A GEOMETRICAL ANALYSIS ON CONVEX CONIC REFORMULATIONS OF QUADRATIC AND POLYNOMIAL OPTIMIZATION PROBLEMS
- 주제(키워드) completely positive programming reformulation , quadratic programs , polynomial optimization problems , conic optimization problems , faces of the completely positive cone
- 주제(기타) Mathematics, Applied
- 설명문(일반) [Kim, Sunyoung] Ewha W Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea; [Kojima, Masakazu] Chuo Univ, Dept Ind & Syst Engn, Tokyo 1920393, Japan; [Toh, Kim-Chuan] Natl Univ Singapore, Dept Math, 10 Lower Kent Ridge Rd, Singapore 119076, Singapore; [Toh, Kim-Chuan] Natl Univ Singapore, Inst Operat Res & Analyt, 10 Lower Kent Ridge Rd, Singapore 119076, Singapore
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SIAM PUBLICATIONS
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000174985
- 본문언어 영어
- Published As http://dx.doi.org/10.1137/19M1237715
초록/요약
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.
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