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The Price of Robustness
TLDR
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
Introduction to linear optimization
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
Robust discrete optimization and network flows
TLDR
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
Theory and Applications of Robust Optimization
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 theExpand
Optimal control of execution costs
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 beExpand
Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem
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 ofExpand
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
TLDR
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
Best Subset Selection via a Modern Optimization Lens
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 MixedExpand
A Robust Optimization Approach to Inventory Theory
TLDR
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
Revenue Management in a Dynamic Network Environment
TLDR
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
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