difference-of-convex program

Algorithms for Difference-of-Convex (DC) Programs Based on Difference-of-Moreau-Envelopes Smoothing

  • Xu Andy Sun
  • Kaizhao Sun
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this paper we consider minimization of a difference-of-convex (DC) function with and without linear constraints. We first study a smooth approximation of a generic DC function, termed difference-of-Moreau-envelopes (DME) smoothing, where both components of the DC function are replaced by their respective Moreau envelopes. The resulting smooth approximation is shown to be Lipschitz differentiable, … Read more

    Consistency Bounds and Support Recovery of D-stationary Solutions of Sparse Sample Average Approximations

  • Miju Ahn
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    This paper studies properties of the d(irectional)-stationary solutions of sparse sample average approximation (SAA) problems involving difference-of-convex (dc) sparsity functions under a deterministic setting. Such properties are investigated with respect to a vector which satisfies a verifiable assumption to relate the empirical SAA problem to the expectation minimization problem defined by an underlying data distribution. … Read more