Convex programming

Data-driven distributionally robust optimization: Intersecting ambiguity sets, performance analysis and tractability

  • Neda Tanoumand
  • Merve Bodur
  • Joe Naoum-Sawaya
    • Categories Robust Optimization Tags , , ,

    We consider stochastic programs in which the probability distribution of uncertain parameters is unknown and partial information about it can only be captured from limited data. We use distributionally robust optimization (DRO) to model such problems. As opposed to the commonly used approach for DRO problems that suggests creating an ambiguity set by following a specific … Read more

    Faster Lagrangian-based methods: a unified prediction-correction framework

  • Zhang Tao
  • Xia Yong
  • Li Shiru
    • Categories Convex Optimization Tags , , ,

    Motivated by the prediction-correction framework constructed by He and Yuan [SIAM J. Numer. Anal. 50: 700-709, 2012], we propose a unified prediction-correction framework to accelerate Lagrangian-based methods. More precisely, for strongly convex optimization, general linearized Lagrangian method with indefinite proximal term, alternating direction method of multipliers (ADMM) with the step size of Lagrangian multiplier not … Read more

    A decomposition method for lasso problems with zero-sum constraint

  • Andrea Cristofari
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses … Read more

    Algebraic-based primal interior-point algorithms for stochastic infinity norm optimization

  • Baha Alzalg
  • Karima Tamsaouete
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We study the two-stage stochastic infinity norm optimization problem with recourse. First, we study and analyze the algebraic structure of the infinity norm cone, and use its algebra to compute the derivatives of the barrier recourse functions. Then, we show that the barrier recourse functions and the composite barrier functions for this optimization problem are … Read more