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math.OC2025
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…
math.OC2025
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…
math.OC2025
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…