5 papers
Maximal monotonicity of piecewise polyhedral mappings
Xudong Li, R. Tyrrell Rockafellar, Defeng Sun
Maximally monotone mappings that are piecewise polyhedral arise from subdifferentials of convex functions and saddle functions that are piecewise linear-quadratic and enter into al…
A Semismooth Newton Augmented Lagrangian Method for Sparse Spectral Risk Optimization
Rufeng Xiao, Rujun Jiang, Xudong Li +1
Empirical risk minimization is a standard and effective paradigm for learning predictive models by minimizing average loss. In high-stakes decision-making, however, an average-loss…
A symmetric Gauss-Seidel based alternating proximal ALM for generalized Nash Equilibrium problems in Banach spaces
Defeng Sun, Hailing Wang, Wei Zhao
In this paper, we study a class of monotone generalized Nash equilibrium problems (GNEPs) with jointly linear constraints. The players' strategy spaces are real Hilbert spaces, whi…
A Level Set Method with Secant Iterations for the Least-Squares Constrained Nuclear Norm Minimization
Chiyu Ma, Jiaming Ma, Defeng Sun
We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a le…
Adaptive sieving: A dimension reduction technique for sparse optimization problems
Yancheng Yuan, Meixia Lin, Defeng Sun +1
In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, whe…