Robust Optimization

From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

  • Wenqing Chen
  • Jie Sun
  • Chung-Piaw Teo
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more

    A New Cone Programming Approach for Robust Portfolio Selection

  • Zhaosong Lu
    • Categories Applications - Science and Engineering, Finance and Economics, Robust Optimization Tags ,

    The robust portfolio selection problems have recently been studied by several researchers (e.g., see \cite{GoIy03,ErGoIy04,HaTu04,TuKo04}). In their work, the “separable” uncertainty sets of the problem parameters (e.g., mean and covariance of the random returns) were considered. These uncertainty sets share two common drawbacks: i) the actual confidence level of the uncertainty set is unknown, and … Read more

    Cascading – An adjusted exchange method for robust conic programming

  • Ralf Werner
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Semi-infinite Programming Tags , ,

    It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski [2] increases the numerical complexity of the solution compared to the original problem. Kocvara, Nemirovski and Zowe therefore introduced in [9] an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show … Read more

    Decentralized Decision-making and Protocol Design for Recycled Material Flows

  • Jane Ammons
  • I-Hsuan Hong
  • Matthew Realff
    • Categories Game Theory, Production and Logistics, Robust Optimization

    Reverse logistics networks often consist of several tiers with independent members competing at each tier. This paper develops a methodology to examine the individual entity behavior in reverse production systems where every entity acts to maximize its own benefits. We consider two tiers in the network, collectors and processors. The collectors determine individual flow functions … Read more

    Portfolio Selection with Robust Estimation

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Finance and Economics, Robust Optimization Tags , , ,

    Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which … Read more

    On Safe Tractable Approximations of Chance Constrained Linear Matrix Inequalities

  • Aharon Ben-Tal
  • Arkadi Nemirovski
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , ,

    In the paper, we consider the chance constrained version $$ \Prob\{A_0[x]+\sum_{i=1}^d\zeta_i A_i[x]\succeq0\}\geq1-\epsilon, $$ of an affinely perturbed Linear Matrix Inequality constraint; here $A_i[x]$ are symmetric matrices affinely depending on the decision vector $x$, and $\zeta_1,…,\zeta_d$ are independent of each other random perturbations with light tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing … Read more

    Selected Topics in Robust Convex Optimization

  • Aharon Ben-Tal
  • Arkadi Nemirovski
    • Categories Control Applications, Robust Optimization, Stochastic Programming Tags , , ,

    Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-but-bounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of {\sl robust counterpart} of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links … Read more

    A New Stochastic Algorithm for Engineering Optimization Problems

  • Tran Van Hao
  • Nguyen Huu Thong
    • Categories Constrained Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags ,

    This paper proposes a new stochastic algorithm, Search via Probability (SP) algorithm, for single-objective optimization problems. The SP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each iteration, and on the performance of SP algorithm we … Read more

    Asynchronous parallel generating set search for linearly-constrained optimization

  • Joshua D. Griffin
  • Robert Michael Lewis
  • Tamara Kolda
    • Categories Constrained Nonlinear Optimization, Parallel Algorithms, Robust Optimization Tags , , , , , , , ,

    Generating set search (GSS) is a family of direct search methods that encompasses generalized pattern search and related methods. We describe an algorithm for asynchronous linearly-constrained GSS, which has some complexities that make it different from both the asynchronous bound-constrained case as well as the synchronous linearly-constrained case. The algorithm has been implemented in the … Read more

    Goal Driven Optimization

  • Wenqing Chen
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Achieving a targeted objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion}, which encompasses the probability of success in achieving the goal and an expected level of under-performance … Read more