An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.Expand

p. 27, l. −11, replace “Schwartz” by “Schwarz” p. 69, l. −13: “ai∗x = bi” should be “ai∗x = bi∗” p. 126, l. 16, replace “inequality constraints” by “linear inequality constraints” p. 153, l. −8,… Expand

This work proposes a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation, and proposes an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.Expand

In this paper we survey the primary research, both theoretical and applied, in the area of robust optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the… Expand

We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block SM of shares to be… Expand

Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of… Expand

It is shown that it is NP-hard to find tight bounds for k = 2 and $\Omega={\cal R}^n$, and an efficient algorithm for finding tight bounds when S is a union of convex sets, over which convex quadratic functions can be optimized efficiently.Expand

In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed… Expand

It is shown that the structure of the optimal robust policy is of the same base-stock character as the optimal stochastic policy for a wide range of inventory problems in single installations, series systems, and general supply chains.Expand

This work proposes and analyzes a new algorithm based on approximate dynamic programming that uses adaptive, nonadditive bid prices from a linear programming relaxation, and reports encouraging computational results that show that the new algorithm leads to higher revenues and more robust performance than bid-price control.Expand