5 papers
Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
Lei Huang, Jiawang Nie, Jiajia Wang +1
This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality condi…
Optimization over the weakly Pareto set and multi-task learning
Lei Huang, Jiawang Nie, Jiajia Wang
We study the optimization problem over the weakly Pareto set of a convex multiobjective optimization problem given by polynomial functions. Using Lagrange multiplier expressions an…
Finite convergence of the Moment-SOS hierarchy for polynomial matrix optimization
Lei Huang, Jiawang Nie
This paper studies the matrix Moment-SOS hierarchy for solving polynomial matrix optimization. Our first result is to show the finite convergence of this hierarchy, if the nondegen…
Finite convergence of Moment-SOS relaxations with non-real radical ideals
Lei Huang, Jiawang Nie, Ya-Xiang Yuan
We consider the linear conic optimization problem with the cone of nonnegative polynomials. Its dual optimization problem is the generalized moment problem. Moment-SOS relaxations…
Moment-SOS relaxations for moment and tensor recovery problems
Lei Huang, Jiawang Nie, Jiajia Wang
This paper studies moment and tensor recovery problems whose decomposing vectors are contained in some given semialgebraic sets. We propose Moment-SOS relaxations with generic obje…