isolated calmness

Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

  • Huy Chieu Nguyen
  • Le Van Hien
    • Categories Nonsmooth Optimization Tags , , , ,

    Let $\Gamma:=\{x\in \R^n\, |\, q(x)\in\Theta\},$ where $q: \R^n\rightarrow\R^m$ is a twice continuously differentiable mapping, and $\Theta$ is a nonempty polyhedral convex set in $\R^m.$ In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping $N_\Gamma:\R^n\rightrightarrows\R^n,$ $x\mapsto N_\Gamma(x),$ under the condition that $M_q(x):=q(x)-\Theta$ is metrically subregular at … Read more

    Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming

  • Deren Han
  • Defeng Sun
  • Liwei Zhang
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain error bound condition, we establish the global linear rate of convergence for a more general semi-proximal ADMM with the dual steplength … Read more

    Calmness modulus of linear semi-infinite programs

  • M.J. Cánovas
  • Alexander Y. Kruger
  • Marco A. López
  • J. Parra
  • Michel Thera
    • Categories Linear Programming, Semi-infinite Programming Tags , , , ,

    Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide … Read more

    Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability

  • Boris S. Mordukhovich
  • Jiri V. Outrata
  • Héctor Ramírez
    • Categories Convex and Nonsmooth Optimization Tags , , , , , ,

    This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized di erential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related … Read more