A Parallel Bundle Framework for Asynchronous Subspace Optimisation of Nonsmooth Convex Functions

  • Frank Fischer
  • Christoph Helmberg
    • Categories Convex and Nonsmooth Optimization, Parallel Algorithms Tags , ,

    An algorithmic framework is presented for optimising general convex functions by non synchronised parallel processes. Each process greedily picks a suitable adaptive subset of coordinates and runs a bundle method on a corresponding restricted problem stopping whenever a descent step is encountered or predicted decrease is reduced sufficiently. No prior knowledge on the dependencies between … Read more

    New Analysis and Results for the Conditional Gradient Method

  • Robert M. Freund
  • Paul Grigas
    • Categories Convex Optimization Tags , , , ,

    We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial … Read more

    An approximation scheme for a class of risk-averse stochastic equilibrium problems

  • Juan Pablo Luna
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , , , ,

    We consider two models for stochastic equilibrium: one based on the variational equilibrium of a generalized Nash game, and the other on the mixed complementarity formulation. Each agent in the market solves a one-stage risk-averse optimization problem with both here-and-now (investment) variables and (production) wait-and-see variables. A shared constraint couples almost surely the wait-and-see decisions … Read more

    Extended Linear Formulation for Binary Quadratic Problems

  • Fabio Furini
  • Emiliano Traversi
    • Categories 0-1 Programming, Quadratic Programming

    In this work we propose and test a new linearisation technique for Binary Quadratic Problems (BQP). We computationally prove that the new formulation, called Extended Linear Formulation, performs much better than the standard one in practice, despite not being stronger in terms of Linear Programming relaxation (LP). We empirically prove that this behaviour is due … Read more

    Sample Average Approximation Method for Compound Stochastic Optimization Problems

  • Yuri M. Ermoliev
  • Vladimir I. Norkin
    • Categories Statistics, Stochastic Programming

    The paper studies stochastic optimization (programming) problems with compound functions containing expectations and extreme values of other random functions as arguments. Compound functions arise in various applications. A typical example is a variance function of nonlinear outcomes. Other examples include stochastic minimax problems, econometric models with latent variables, and multilevel and multicriteria stochastic optimization problems. … Read more

    On Minimal Valid Inequalities for Mixed Integer Conic Programs

  • Fatma Kılınç-Karzan
    • Categories (Mixed) Integer Nonlinear Programming

    We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient … Read more

    Finitely Convergent Decomposition Algorithms for Two-Stage Stochastic Pure Integer Programs

  • Simge Küçükyavuz
  • Minjiao Zhang
    • Categories Integer Programming, Stochastic Programming Tags , ,

    We study a class of two-stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Gomory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision variables, … Read more

    Family Constraining of Iterative Algorithms

  • Yair Censor
  • Ioana Pantelimon
  • Constantin Popa
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares Tags , ,

    In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image … Read more

    Randomized Block Coordinate Non-Monotone Gradient Method for a Class of Nonlinear Programming

  • Zhaosong Lu
  • Lin Xiao
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    In this paper we propose a randomized block coordinate non-monotone gradient (RBCNMG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and typically solves several associated proximal subproblems that usually have … Read more

    Mixed Integer Second-Order Cone Programming Formulations for Variable Selection

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , , ,

    This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the … Read more