An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization

We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new algorithmic framework that blends local search using the...

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Bibliographic Details
Published in:	Mathematical programming Vol. 201; no. 1-2; pp. 409 - 472
Main Authors:	Yang, Heng, Liang, Ling, Carlone, Luca, Toh, Kim-Chuan
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023 Springer
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Methods Numerical Analysis Theoretical Semidefinite programming Degeneracy Polynomial optimization 90C22 90C55 90C23 90C06 Nonlinear programming Inexact projected gradient method Rank-one solutions
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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