Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part II: Complexity and Numerical Results

  • Loris Cannelli
  • Francisco Facchinei
  • Vyacheslav Kungurtsev
  • Gesualdo Scutari
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Parallel Algorithms Tags , , ,

    We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of … Read more

    Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part I: Model and Convergence

  • Loris Cannelli
  • Francisco Facchinei
  • Vyacheslav Kungurtsev
  • Gesualdo Scutari
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Parallel Algorithms Tags , , ,

    We propose a novel asynchronous parallel algorithmic framework for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous … Read more

    Risk-based Loan Pricing: Portfolio Optimization Approach With Marginal Risk Contribution

  • So Yeon Chun
  • Miguel A. Lejeune
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , , , ,

    We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more

    Semidefinite Programming Approach to Russell Measure Model

  • Margaréta Halická
  • Mária Trnovská
    • Categories Applications - OR and Management Sciences, Semi-definite Programming

    Throughout its evolution, data envelopment analysis (DEA) has mostly relied on linear programming, particularly because of simple primal-dual relations and the existence of standard software for solving linear programs. Although also non-linear models, such as Russell measure or hyperbolic measure models, have been introduced, their use in applications has been limited mainly because of their … Read more

    Data-Driven Optimization of Reward-Risk Ratio Measures

  • Ran Ji
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more

    Data-Driven Optimization of Reward-Risk Ratio Measures

  • Ran Ji
  • Miguel A. Lejeune
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more

    High-dimensional risk-constrained dynamic asset allocation via Markov stochastic dual dynamic programming

  • Marcus Poggi de Aragão
  • Thuener Silva
  • Davi Valladão
    • Categories Finance and Economics, Stochastic Programming Tags , , ,

    Dynamic portfolio optimization has a vast literature exploring different simplifications by virtue of computational tractability of the problem. Previous works provide solution methods considering unrealistic assumptions, such as no transactional costs, small number of assets, specific choices of utility functions and oversimplified price dynamics. Other more realistic strategies use heuristic solution approaches to obtain suitable … Read more

    Distributionally Robust Stochastic Optimization with Dependence Structure

  • Anton J. Kleywegt
  • Rui Gao
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for specifying a set of distributions have been proposed. The choice matters, because it affects the results, and the relative performance of different choices depend on … Read more

    Worst-Case Expected Shortfall with Univariate and Bivariate Marginals

  • Bikramjit Das
  • Karthik Natarajan
  • Anulekha Dhara
    • Categories Finance and Economics Tags , , ,

    Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate … Read more

    Scenario Reduction Revisited: Fundamental Limits and Guarantees

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Kilian Schindler
  • Wolfram Wiesemann
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure … Read more