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A more efficient reformulation of complex SDP as real SDP
Jie Wang
This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of…
Solving Low-Rank Semidefinite Programs via Manifold Optimization
Jie Wang, Liangbing Hu
We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions, with an emphasis on SDP relaxations for polynomial optimization pro…
Exploiting Sparsity in Complex Polynomial Optimization
Jie Wang, Victor Magron
In this paper, we study the sparsity-adapted complex moment-Hermitian sum of squares (moment-HSOS) hierarchy for complex polynomial optimization problems, where the sparsity includ…
SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming
Victor Magron, Jie Wang
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in th…
A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients
Jie Wang, Victor Magron
This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lowe…