scholarly journals Distributionally Robust Joint Chance Constrained Problem under Moment Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ke-wei Ding
Keyword(s):  
Semidefinite Programming ◽  
Chance Constraints ◽  
Second Order ◽  
Quadratic Approximation ◽  
Convex Approximation ◽  
Worst Case ◽  
Constrained Problem ◽  
Distributionally Robust

We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.

scholarly journals Distributionally robust joint chance constraints with second-order moment information

2011 ◽  
Vol 137 (1-2) ◽  
pp. 167-198 ◽  
Author(s):  
Steve Zymler ◽  
Daniel Kuhn ◽  
Berç Rustem
Keyword(s):  
Chance Constraints ◽  
Second Order ◽  
Order Moment ◽  
Distributionally Robust

scholarly journals Energy and reserve dispatch with distributionally robust joint chance constraints

2021 ◽  
Vol 49 (3) ◽  
pp. 291-299 ◽  
Author(s):  
Christos Ordoudis ◽  
Viet Anh Nguyen ◽  
Daniel Kuhn ◽  
Pierre Pinson
Keyword(s):  
Chance Constraints ◽  
Distributionally Robust

Safe Approximations for Distributionally Robust Joint Chance Constrained Program

2015 ◽  
Vol 32 (01) ◽  
pp. 1540004 ◽  
Author(s):  
Chenchen Wu ◽  
Dachuan Xu ◽  
Jiawei Zhang
Keyword(s):  
Covariance Matrix ◽  
Second Order ◽  
Uncertain Parameters ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Numerical Tests ◽  
Second Order Cone ◽  
Distributionally Robust ◽  
Interval Constraint

In this paper, we present a bilinear second-order cone programming safe approximation for the distributionally robust chance constrained program (DRCCP), assuming that the support of the uncertain parameters, and the first and second marginal moments of the probability with respect to the interval constraint imposed on the sum of the uncertain parameters are given. If we further know the covariance matrix, we can obtain a bilinear semi-definite programming safe approximation. Preliminary numerical tests indicate that the proposed models are competitive.

A Second Order Approximation Technique for Robust Shape Optimization

2011 ◽  
Vol 104 ◽  
pp. 13-22 ◽  
Author(s):  
Adrian Sichau ◽  
Stefan Ulbrich
Keyword(s):  
Shape Optimization ◽  
Order Approximation ◽  
Trust Region ◽  
State Equation ◽  
Second Order ◽  
Approximation Technique ◽  
Worst Case ◽  
Second Order Approximation ◽  
Robust Counterpart ◽  
Adjoint Approach

We present a second order approximation for the robust counterpart of general uncertain nonlinear programs with state equation given by a partial di erential equation.We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved effciently using adjoint techniques. Further, we describe how the gradients of the worst-case functions can be computed analytically combining a sensitivity and an adjoint approach. This methodis applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainty in acting forces. Numerical results are presented.

scholarly journals The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Liyan Xu ◽  
Bo Yu ◽  
Wei Liu
Keyword(s):  
Robust Optimization ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Uncertain Parameters ◽  
Distributionally Robust Optimization ◽  
Worst Case ◽  
Nonnegativity Constraints ◽  
Distributionally Robust ◽  
Stochastic Linear Complementarity Problem

We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable.

scholarly journals AUV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Wei Wang ◽  
Ming Jin ◽  
Shanghua Li ◽  
Xinyu Cao
Keyword(s):  
Exact Penalty ◽  
Maximum Eigenvalue ◽  
Convex Approximation ◽  
Equivalent Problem ◽  
Composite Function ◽  
Primal Problem ◽  
Approximate Problem ◽  
Constrained Problem ◽  
Constrained Minimization Problem ◽  
Unconstrained Problem

In this paper, we apply theUV-algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to applyUV-algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and theU-Lagrangian of the object function at a given point will be addressed particularly. Finally, theUV-algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem.

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