Sensitivity Analysis Of Optimization Problems Research Articles

Sensitivity Analysis of the Value Function for Optimization Problems with Variational Inequality Constraints

In this paper we perform sensitivity analysis for optimization problems with variational inequality constraints (OPVICs). We provide upper estimates for the limiting subdifferential (singular limiting subdifferential) of the value function in terms of the set of normal (abnormal) coderivative (CD) multipliers for OPVICs. For the case of optimization problems with complementarity constraints (OPCCs), we provide upper estimates for the limiting subdifferentials in terms of various multipliers. An example shows that the other multipliers may not provide useful information on the subdifferentials of the value function, while the CD multipliers may provide tighter bounds. Applications to sensitivity analysis of bilevel programming problems are also given.

Sensitivity analysis for optimization problems solved by stochastic methods

The problem of obtaining sensitivity analysis information from optimization stochastic methods is addressed in this work, The sensitivity analysis calculation is obtained using the evaluations of the objective function as samples of the behavior of the objective function in the vicinity of the optimum, A linear optimization problem is formulated for the approximation of a contour surface of the objective function in the vicinity of the optimum, The formulation is applied to TEAM benchmark problems 25 and 22. The results, which are in good agreement with the literature, show the applicability of the formulation in practical optimization problems.

Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints

We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization. We derive Lipschitz and Hölder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization.

Shape Design Sensitivity Analysis for Optimization Problems with Local and Global Functionals

ABSTRACT In this paper, problems of sensitivity analysis and shape design for elastic solids are investigated. Optimization criteria are provided by integral and local functionals defined on the internal region and the boundary of the body. New sensitivity analysis relations are derived and implemented in successive optimization algorithms. Important aspects of effective shape optimization algorithms are discussed.

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

A family of optimization problems in a Hilbert space depending on a vector parameter is considered. It is assumed that the problems have locally isolated local solutions. Both these solutions and the associated Lagrange multipliers are assumed to be locally Lipschitz continuous functions of the parameter. Moreover, the assumption of the type of strong second-order sufficient condition is satisfied.

Duality and Sensitivity Analysis for Fractional Programs

In this paper we consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective function is the ratio of two real-valued functions. We discuss a procedure suggested by Dinkelbach for solving the problem, its relation to certain approaches via variable transformations, and a variant of the procedure that has convenient convergence properties. The duality correspondences that are developed do not require either differentiability or the existence of an optimal solution. The sensitivity analysis applies to linear fractional problems, even when they “solve” at an extreme ray, and includes a primal-dual algorithm for parametric right-hand-side analysis.