This paper proposes a robust optimization model for optimal self scheduling of a hydro-thermal generating company. The proposed model is suitable for price taker Gencos which seeks the optimal schedule of its thermal and hydro generating units for a given operating horizon. The uncertainties of electricity prices are modeled using robust optimization approach to make … Read more
We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. In addition to many practical advantages, due to the flexibility of our approach, we are able to prove that the robust optimal solutions generated by our algorithms are at least as desirable … Read more
We address robust versions of combinatorial optimization problems, focusing on the uncorrelated ellipsoidal uncertainty case, which corresponds to so-called mean-variance optimization. We present a branch and bound-algorithm for such problems that uses lower bounds obtained from Lagrangean decomposition. This approach allows to separate the uncertainty aspect in the objective function from the combinatorial structure of … Read more
We study the Minimax Regret Uncapacitated Lot Sizing (MRULS) model, where the production cost function and the demand are subject to uncertainty. We propose a polynomial time algorithm which solves the MRULS model in O(n^6) time. We improve this running time to O(n^5) when only the demand is uncertain, and to O(n^4) when only the … Read more
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
In this paper, we introduce a framework for derivative-free robust optimization based on the use of an efficient derivative-free optimization routine for mixed integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC-DC converter commonly used in portable electronic devices). The proposed robust … Read more
In stochastic optimal control the distribution of the exogenous noise is typically unknown and must be inferred from limited data before dynamic programming (DP)-based solution schemes can be applied. If the conditional expectations in the DP recursions are estimated via kernel regression, however, the historical sample paths enter the solution procedure directly as they determine … Read more
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as linear programs (LPs) and semidefinite programs (SDPs). A CGP consists of a linear objective function that is to be minimized subject to affine constraints, convex conic constraints, and upper bound constraints … Read more
The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact semi-definite linear programming relaxation (SDP-relaxation) and strong duality. Unfortunately, such properties do not, in general, hold for an extended trust-region problem having … Read more
Probabilistic programs are widely used decision models. When implemented in practice, however, there often exists distributional ambiguity in these models. In this paper, we model the ambiguity using the likelihood ratio (LR) and use LR to construct various ambiguity sets. We consider ambiguous probabilistic programs which optimize under the worst case. Ambiguous probabilistic programs can … Read more