semidenite programming

A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

  • Jianqiang Cheng
  • Miguel A. Lejeune
  • Roya Karimi
    • Categories Stochastic Programming Tags , , , ,

    We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix, and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions ensuring convexity. … Read more

    Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Kilian Schindler
  • Wolfram Wiesemann
    • Categories Approximation Algorithms, Data-Mining, Linear, Cone and Semidefinite Programming Tags , , ,

    Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier-detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outlier cluster and performs cardinality-constrained K-means clustering on the residual dataset. We cast this problem as a mixed-integer … Read more

    On bounding the bandwidth of graphs with symmetry

  • Renata Sotirov
  • Edwin van Dam
    • Categories Semi-definite Programming Tags , , , , ,

    We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semide finite programming relaxation of the minimum cut problem is obtained by strengthening the well-known semide nite programming relaxation for the quadratic assignment problem by fixing two vertices in the … Read more

    Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets” [Optim. Letters, 2012]

  • Peter J.C. Dickinson
  • Gabriele Eichfelder
  • Janez Povh
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper, an erratum is provided to the article “\emph{On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets}”, published in Optim.\ Letters, 2012. Due to precise observation of the first author, it has been found that the proof of Lemma 9 has a nontrivial gap, and consequently the main result (Theorem … Read more