2 citations · 2 across the 10 of their papers we have counts for
11 papers
Rank One Completion for Higher Order Tensors
Linghao Zhang, Ioana Dumitriu, Jiawang Nie
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursi…
Learning Polynomial Activation Functions for Deep Neural Networks
Linghao Zhang, Jiawang Nie, Tingting Tang
Activation functions are crucial for deep neural networks. This novel work frames the problem of training neural network with learnable polynomial activation functions as a polynom…
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…
Sparse Polynomial Optimization with Matrix Constraints
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient a…
A Characterization for Tightness of the Sparse Moment-SOS Hierarchy
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if th…
Polynomial Optimization Over Unions of Sets
Jiawang Nie, Linghao Zhang
This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxa…
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…
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…
Solving polynomial variational inequality problems via Lagrange multiplier expressions and Moment-SOS relaxations
Jiawang Nie, Defeng Sun, Xindong Tang +1
In this paper, we study variational inequality problems (VIPs) with involved mappings and feasible sets characterized by polynomial functions (namely, polynomial VIPs). We propose…