The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or … Read more
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value when the stochastic program is expressed in terms of a law invariant coherent risk measure having a discrete Kusuoka representation. The obtained results … Read more
This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear approximation method. Our results show … Read more
In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of … Read more
We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader’s problem. Both bounding problems are equivalent to explicit mixed-integer linear programs … Read more
We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more
We consider decision making problems under uncertainty, assuming that only partial distributional information is available – as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be … Read more
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of … Read more
In various settings time consistency in dynamic programming has been addressed by many authors going all the way back to original developments by Richard Bellman. The basic idea of the involved dynamic principle is that a policy designed at the first stage, before observing realizations of the random data, should not be changed at the … Read more
Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the LP relaxation, and a randomization step used when the algorithm stalls. While many generalizations and improvements to the original Feasibility Pump have … Read more