Asymptotical Analysis of a SAA Estimator for Optimal Value of a Two Stage Problem with Quadratic Recourse∗
نویسندگان
چکیده
In this paper, we first consider the stability analysis of a convex quadratic programming problem and its restricted Wolfe dual in which all parameters in the problem are perturbed. We demonstrate the upper semi-continuity of solution mappings for the primal problem and the restricted Wolfe dual problem and establish the Hadamard directionally differentiability of the optimal value function. By expressing the optimal value function as a min-max optimization problem over two compact convex sets, we present the asymptotic distribution of a SAA estimator of the optimal value for a two stage program whose second stage problem is a convex quadratic programming problem and all parameters in the quadratic program are random variables.
منابع مشابه
Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations...
متن کاملDiscrete-time repetitive optimal control: Robotic manipulators
This paper proposes a discrete-time repetitive optimal control of electrically driven robotic manipulators using an uncertainty estimator. The proposed control method can be used for performing repetitive motion, which covers many industrial applications of robotic manipulators. This kind of control law is in the class of torque-based control in which the joint torques are generated by permanen...
متن کاملDetermining the Optimal Value Bounds of the Objective Function in Interval Quadratic Programming Problem with Unrestricted Variables in Sign
In the most real-world applications, the parameters of the problem are not well understood. This is caused the problem data to be uncertain and indicated with intervals. Interval mathematical models include interval linear programming and interval nonlinear programming problems.A model of interval nonlinear programming problems for decision making based on uncertainty is interval quadratic prog...
متن کاملMixed two-stage derivative estimator for sensitivity analysis
In mathematical modeling, determining most influential parameters on outputs is of major importance. Thus, sensitivity analysis of parameters plays an important role in model validation. We give detailed procedure of constructing a new derivative estimator for general performance measure in Gaussian systems. We will take advantage of using score function and measure-value derivative estimators ...
متن کاملOptimal Process Planning under Uncertainty with Risk Management
We propose a computationally-tractable optimization-based framework for risk management in midterm process planning under uncertainty. We employ stochastic programming to account for the uncertainty in which a scenario-based approach is used to represent the underlying probability distribution of the uncertain parameters. The problem is formulated as a two-stage stochastic program with recourse...
متن کامل