84 citations · 160 across the 18 of their papers we have counts for
21 papers
Strengthened Complex Moment Hierarchies and Finite Convergence over Spheres
Jie Wang
This paper proposes strengthened complex moment relaxations for complex polynomial optimization. The proposed relaxation augments the pruned complex moment relaxation with selected…
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…
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…
State polynomials: positivity, optimization and nonlinear Bell inequalities
Igor Klep, Victor Magron, Jurij Volčič +1
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin's solution to Hilbert's 17th probl…
Sparse Polynomial Optimization: Theory and Practice
Victor Magron, Jie Wang
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can conv…
Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems
Jie Wang, Corbinian Schlosser, Milan Korda +1
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computat…
Certifying Global Optimality of AC-OPF Solutions via sparse polynomial optimization
Jie Wang, Victor Magron, Jean B. Lasserre
We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy -- a moment-SOS based hierarchy that ex…
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…
TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization
Victor Magron, Jie Wang
The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting corr…
Stability of Linear Systems under Extended Weakly-Hard Constraints
Nils Vreman, Paolo Pazzaglia, Jie Wang +2
Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when…
Exploiting constant trace property in large-scale polynomial optimization
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron +1
We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matri…
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…
Exploiting term sparsity in Noncommutative Polynomial Optimization
Jie Wang, Victor Magron
We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy feat…
SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions
Jie Wang, Martina Maggio, Victor Magron
This paper focuses on the computation of joint spectral radii (JSR), when the involved matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and Jad…
CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
Jie Wang, Victor Magron, Jean B. Lasserre +1
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlativ…
Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
Jie Wang, Victor Magron, Jean-Bernard Lasserre
This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sp…
TSSOS: A Moment-SOS hierarchy that exploits term sparsity
Jie Wang, Victor Magron, Jean-Bernard Lasserre
This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of s…
A second order cone characterization for sums of nonnegative circuits
Jie Wang, Victor Magron
The second-order cone 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 theory a…
A New Sparse SOS Decomposition Algorithm Based on Term Sparsity
Jie Wang, Haokun Li, Bican Xia
A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and…
On -Tensors
Zheng-Hai Huang, Yun-Yang Suo, Jie Wang
One of the central problems in the theory of linear complementarity problems (LCPs) is to study the class of -matrices since it characterizes the solvability of LCP. Recently, t…