A note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation

In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we … Read more

Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class … Read more

AN-SPS: Adaptive Sample Size Nonmonotone Line Search Spectral Projected Subgradient Method for Convex Constrained Optimization Problems

Article Download View AN-SPS: Adaptive Sample Size Nonmonotone Line Search Spectral Projected Subgradient Method for Convex Constrained Optimization Problems

A Simplified Convergence Theory for Byzantine Resilient Stochastic Gradient Descent

In distributed learning, a central server trains a model according to updates provided by nodes holding local data samples. In the presence of one or more malicious servers sending incorrect information (a Byzantine adversary), standard algorithms for model training such as stochastic gradient descent (SGD) fail to converge. In this paper, we present a simplified … Read more