9 papers · 1 filter
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…