Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures

  • Vincent Guigues
  • Werner Romisch
    • Categories Stochastic Programming

    We define a risk averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk averse formulation of the problem. This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of … Read more

    On the acceleration of augmented Lagrangian method for linearly constrained optimization

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , ,

    The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic development of constrained optimization. In this paper, we mainly show that Nesterov’s influential acceleration techniques can be applied to accelerate ALM, thus yielding an accelerated ALM whose iteration-complexity is O(1/k^2) for linearly constrained convex programming. As a by-product, we also show easily that … Read more

    Portfolio Selection under Model Uncertainty: A Penalized Moment-Based Optimization Approach

  • Roy H. Kwon
  • Jonathan Y. Li
    • Categories Finance and Economics, Robust Optimization, Semi-definite Programming Tags ,

    We present a new approach for portfolio selection when the underlying distribution of asset returns is uncertain or ambiguous to investors. In particular, we consider the case that an investor can formulate some reference financial models based on his/her prior beliefs or information, but is concerned about misspecification of the reference models and the associated … Read more

    Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

    Total variation superiorization schemes in proton computed tomography image reconstruction

  • Yair Censor
  • Scott Penfold
  • Anatoly Rosenfeld
  • Reinhard W. Schulte
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Other Topics Tags ,

    Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, noise in the reconstructed image increases with successive iterations. In the current work, we investigated the use of total variation superiorization (TVS) … Read more

    Quest for the control on the second order derivatives: topology optimization with functional includes the state’s curvature

  • Rouhollah Tavakoli
    • Categories Distributed Control, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , ,

    Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to consistently control the underlaying process. However, this type of control is nontrivial and to the best … Read more

    Comparing SOS and SDP relaxations of sensor network localization

  • João Gouveia
  • Ting Kei Pong
    • Categories Semi-definite Programming Tags , , ,

    We investigate the relationships between various sum of squares (SOS) and semidefinite programming (SDP) relaxations for the sensor network localization problem. In particular, we show that Biswas and Ye’s SDP relaxation is equivalent to the degree one SOS relaxation of Kim et al. We also show that Nie’s sparse-SOS relaxation is stronger than the edge-based … Read more

    The value of rolling horizon policies for risk-averse hydro-thermal planning

  • Vincent Guigues
  • Claudia Sagastizábal
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming

    We consider the optimal management of a hydro-thermal power system in the mid and long terms. From the optimization point of view, this amounts to a large-scale multistage stochastic linear program, often solved by combining sampling with decomposition algorithms, like stochastic dual dynamic programming. Such methodologies, however, may entail prohibitive computational time, especially when applied … Read more

    A Game-Theoretical Dynamic Model for Electricity Markets

  • Aswin Kannan
  • Victor M. Zavala
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Game Theory Tags , , , , , , ,

    We present a game-theoretical dynamic model for competitive electricity markets.We demonstrate that the model can be used to systematically analyze the effects of ramp constraints, initial conditions, dynamic disturbances, forecast horizon, bidding frequency, and some other factors on the price signals.We illustrate the capabilities of the model using a numerical case study ArticleDownload View PDF

    Minimum weight Topology optimization subject to unsteady heat equation and space-time pointwise constraints — toward automatic optimal riser design in the shape casting process

  • Rouhollah Tavakoli
    • Categories Distributed Control, Mechanical Engineering, Multidisciplinary Design Optimization Tags , , , , ,

    The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient … Read more