Distributionally robust expectation inequalities for structured distributions

  • Paul J. Goulart
  • Bart Paul Gerard Van Parys
  • Manfred Morari
    • Categories Convex Optimization, Semi-definite Programming, Stochastic Programming Tags , , ,

    Quantifying the risk of unfortunate events occurring, despite limited distributional information, is a basic problem underlying many practical questions. Indeed, quantifying constraint violation probabilities in distributionally robust programming or judging the risk of financial positions can both be seen to involve risk quantification, notwithstanding distributional ambiguity. In this work we discuss worst-case probability and conditional … Read more

    On the convergence rate of an inexact proximal point algorithm for quasiconvex minimization on Hadamard manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Global Optimization Tags , , , , ,

    In this paper we present a rate of convergence analysis of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem. ArticleDownload View PDF

    On the convergence of the Sakawa-Shindo algorithm in stochastic control

  • Joseph Frédéric Bonnans
  • J. Gianatti
  • Francisco J. Silva
    • Categories Other Topics Tags , ,

    We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of … Read more

    JuMP: A modeling language for mathematical optimization

  • Iain Dunning
  • Joey Huchette
  • Miles Lubin
    • Categories Modeling Languages and Systems Tags ,

    JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to offer unique functionality while achieving performance on par with commercial modeling tools for standard … Read more

    Search-Enhanced Instantaneous Frequency Detection Algorithm: A Preliminary Design

  • Phen Chiak See
    • Categories Approximation Algorithms

    This paper presents a method developed for finding sinusoidal components within a nonlinear non-stationary time-series data using Genetic Algorithm (GA) (a global optimization technique). It is called Search-Enhanced Instantaneous Frequency Detection (SEIFD) algorithm. The GA adaptively define the configuration of the components by simulating the solution finding process as a series of genetic evolutions. The … Read more

    AN ASYMPTOTIC VISCOSITY SELECTION RESULT FOR THE REGULARIZED NEWTON DYNAMIC

  • Boushra Abbas
    • Categories Nonlinear Optimization

    Let $\Phi:\mathcal{H}\longrightarrow\mathbb{R\cup}\left\{ +\infty\right\} $ be a closed convex proper function on a real Hilbert space $\mathcal{H}$, and $\partial\Phi:\mathcal{H}\rightrightarrows\mathcal{H}$ its subdifferential. For any control function $\epsilon:\mathbb{R}_{+}\longrightarrow\mathbb{R}_{+}$ which tends to zero as $t$ goes to $+\infty$, and $\lambda$ a positive parameter, we study the asymptotic behavior of the trajectories of the regularized Newton dynamical system \begin{eqnarray*} & … Read more

    Robust nonlinear optimization via the dual

  • Dick den Hertog
  • Bram L. Gorissen
    • Categories Robust Optimization Tags

    Robust nonlinear optimization is not as well developed as the linear case, and limited in the constraints and uncertainty sets it can handle. In this work we extend the scope of robust optimization by showing how to solve a large class of robust nonlinear optimization problems. The fascinating and appealing property of our approach is … Read more

    A second-order sequential optimality condition associated to the convergence of optimization algorithms

  • Roberto Andreani
  • Gabriel Haeser
  • Alberto Ramos
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , ,

    Sequential optimality conditions have recently played an important role on the analysis of the global convergence of optimization algorithms towards first-order stationary points and justifying their stopping criteria. In this paper we introduce the first sequential optimality condition that takes into account second-order information. We also present a companion constraint qualification that is less stringent … Read more

    First order optimality conditions for mathematical programs with second-order cone complementarity constraints

  • Jane J. Ye
  • Jinchuan Zhou
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Second-Order Cone Programming Tags , , , , ,

    In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by a second-order cone. We show that if the SOCMPCC is considered as an optimization problem with convex cone constraints, then Robinson’s constraint qualification … Read more

    A Lex-BFS-based recognition algorithm for Robinsonian matrices

  • Monique Laurent
  • Matteo Seminaroti
    • Categories Combinatorial Optimization

    Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be reordered. We present a new polynomial time algorithm to recognize Robinsonian matrices based on a new characterization of Robinsonian matrices in terms of straight enumerations of unit interval graphs. The algorithm … Read more