conic constraints

The Optimal Smoothings of Sublinear Functions and Convex Cones

  • Thabo Samakhoana
  • Benjamin Grimmer
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal smoothings is given. These provide if and only if characterizations of the set of optimal smoothings for … Read more

    An Augmented Lagrangian Method for Conic Convex Programming

  • Necdet Serhat Aybat
  • Garud Iyengar
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min{rho(x)+gamma(x): Ax-b in K, x in chi}, where rho and gamma are closed convex functions, and gamma has a Lipschitz continuous gradient, A is mxn real matrix, K is a closed convex cone, and chi is a “simple” … Read more