Regularized Stochastic Dual Dynamic Programming for convex nonlinear optimization problems

  • Vincent Guigues
  • Miguel A. Lejeune
  • Wajdi Tekaya
    • Categories Dynamic Programming, Finance and Economics, Stochastic Programming Tags , , , ,

    We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming (SDDP) … Read more

    Communication-Efficient Algorithms for Decentralized and Stochastic Optimization

  • Guanghui Lan
  • Soomin Lee
  • Yi Zhou
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , , , , ,

    We present a new class of decentralized first-order methods for nonsmooth and stochastic optimization problems defined over multiagent networks. Considering that communication is a major bottleneck in decentralized optimization, our main goal in this paper is to develop algorithmic frameworks which can significantly reduce the number of inter-node communications. We first propose a decentralized primal-dual … Read more

    Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

  • Giancarlo Bigi
  • Mauro Passacantando
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , ,

    A model for Nash-Cournot oligopolistic markets with concave cost functions and a differentiated commodity is analysed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity … Read more

    Quasi-Newton methods for constrained nonlinear systems: complexity analysis and application

  • Leopoldo Marini
  • Benedetta Morini
  • Margherita Porcelli
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares

    We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several … Read more

    A Penalty Method for Rank Minimization Problems in Symmetric Matrices

  • John E. Mitchell
  • Xin Shen
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Semi-definite Programming Tags , ,

    The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal … Read more

    Quantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization

  • Alois Pichler
  • Huifu Xu
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage. We carry out stability analysis by looking into variations of the ambiguity set under the Wasserstein metric, decision spaces at both stages and the support … Read more

    On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

  • Welington de Oliveira
  • Yongjia Song
  • Wim van Ackooij
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , ,

    We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling … Read more

    Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

  • Yongchao Liu
  • Xinmin Yang
  • Jin Zhang
  • Yong Zhao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more

    Two-stage Stochastic Programming under Multivariate Risk Constraints with an Application to Humanitarian Relief Network Design

  • Simge Küçükyavuz
  • Merve Merakli
  • Nilay Noyan
    • Categories Stochastic Programming

    In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure … Read more

    A Stochastic Programming Approach for Electric Vehicle Charging Network Design

  • Ratna Chinnam
  • Sina Faridimehr
  • Saravanan Venkatachalam
    • Categories Stochastic Programming, Transportation Tags , , ,

    Advantages of electric vehicles (EV) include reduction of greenhouse gas and other emissions, energy security, and fuel economy. The societal benefits of large-scale adoption of EVs cannot be realized without adequate deployment of publicly accessible charging stations. We propose a two-stage stochastic programming model to determine the optimal network of charging stations for a community … Read more