sensitivity analysis

Decision Making Based on a Nonparametric Shape-Preserving Perturbation of a Reference Utility Function

  • Jian Hu
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper develops a robust optimization based decision-making framework using a nonparametric perturbation of a reference utility function. The perturbation preserves the risk-aversion property but solves the problem of ambiguity and inconsistency in eliciting the reference utility function. We study the topology of the perturbation, and show that in the decision-making framework the price of … Read more

    Variational Properties of Value Functions

  • Aleksandr Y. Aravkin
  • James V. Burke
  • Michael P. Friedlander
    • Categories Convex and Nonsmooth Optimization Tags , ,

    Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring question in regularization approaches is the selection of regularization parameters, and its effect on the solution and on the optimal value of the optimization problem. The sensitivity of the value function to the regularization parameter can be linked directly … Read more

    Optimality, identifiability, and sensitivity

  • Dmitriy Drusvyatskiy
  • Adrian Lewis
    • Categories Nonsmooth Optimization Tags , , , , , , , , ,

    Around a solution of an optimization problem, an “identifiable” subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are “minimal”. This new notion lays a broad and intuitive variational-analytic … Read more

    Sensitivity analysis for relaxed optimal control problems with final-state constraints

  • Joseph Frédéric Bonnans
  • Laurent Pfeiffer
  • Oana Silvia Serea
    • Categories Systems governed by Differential Equations Optimization Tags , , , , ,

    In this article, we compute a second-order expansion of the value function of a family of relaxed optimal control problems with final-state constraints, parameterized by a perturbation variable. The sensitivity analysis is performed for controls that we call R-strong solutions. They are optimal solutions with respect to the set of feasible controls with a uniform … Read more

    Sensitivity analysis for the outages of nuclear power plants

  • Kengy Barty
  • Joseph Frédéric Bonnans
  • Laurent Pfeiffer
    • Categories Control Applications Tags , , ,

    Nuclear power plants must be regularly shut down in order to perform refueling and maintenance operations. The scheduling of the outages is the first problem to be solved in electricity production management. It is a hard combinatorial problem for which an exact solving is impossible. Our approach consists in modelling the problem by a two-level … Read more

    Sensitivity analysis for two-level value functions with applications to bilevel programming

  • Stephan Dempe
  • Boris S. Mordukhovich
  • Alain Zemkoho
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , , ,

    This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more dicult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary … Read more

    Partial Smoothness,Tilt Stability, and Generalized Hessians

  • Adrian Lewis
  • Shanshan Zhang
    • Categories Nonsmooth Optimization Tags , , , , , , , ,

    We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition. Article Download View Partial Smoothness,Tilt … Read more

    First order dependence on uncertainty sets in robust optimization

  • C.H. Jeffrey Pang
    • Categories Nonsmooth Optimization, Robust Optimization Tags , , ,

    We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem. Article Download View First order dependence on uncertainty sets in robust optimization

    Necessary Optimality Conditions for two-stage Stochastic Programs with Equilibrium Constraints

  • Huifu Xu
  • Jane J. Ye
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    Developing first order optimality conditions for a two-stage stochastic mathematical program with equilibrium constraints (SMPEC) whose second stage problem has multiple equilibria/solutions is a challenging undone work. In this paper we take this challenge by considering a general class of two-stage whose equilibrium constraints are represented by a parametric variational inequality (where the first stage … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more