Results 1  10
of
36
A Robust Optimization Perspective Of Stochastic Programming
, 2005
"... In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of c ..."
Abstract

Cited by 51 (12 self)
 Add to MetaCart
In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions to a class of stochastic linear optimization problems where the risk of infeasibility can be tolerated as a tradeoff to improve upon the objective value. An attractive feature of the framework is the computational scalability to multiperiod models. We show an application of the framework for solving a project management problem with uncertain activity completion time.
Cuttingset methods for robust convex optimization with pessimizing oracles
 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING, UNIVERSITY OF CALIFORNIA, SAN DIEGO. FROM
, 2011
"... We consider a general worstcase robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worstcase ana ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
(Show Context)
We consider a general worstcase robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worstcase analysis. With exact worstcase analysis, the method is shown to converge to a robust optimal point. With approximate worstcase analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worstcase analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warmstart techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.
Robust portfolios: contributions from operations research and finance
, 2009
"... In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard meanvariance objective, but also in terms of two of the most popu ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard meanvariance objective, but also in terms of two of the most popular risk measures, meanVaR and meanCVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.
Tractable approximate robust geometric programming
 OPTIM ENG
, 2006
"... The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. Robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a GP and optimizing for the worstcase scenario under th ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. Robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a GP and optimizing for the worstcase scenario under this model. However, it is not known whether a general robust GP can be reformulated as a tractable optimization problem that interiorpoint or other algorithms can efficiently solve. In this paper we propose an approximation method that seeks a compromise between solution accuracy and computational efficiency. The method is based on approximating the robust GP as a robust linear program (LP), by replacing each nonlinear constraint function with a piecewiselinear (PWL) convex approximation. With a polyhedral or ellipsoidal description of the uncertain data, the resulting robust LP can be formulated as a standard convex optimization problem that interiorpoint methods can solve. The drawback of this basic method is that the number of terms in the PWL approximations required to obtain an acceptable approximation error can be very large. To overcome the “curse of dimensionality” that arises in directly approximating the nonlinear constraint functions in the original robust GP, we form a conservative approximation of the original robust GP, which contains only bivariate constraint functions. We show how to find globally optimal PWL approximations of these bivariate constraint functions.
Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts
, 2009
"... In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive uncertainties. We propose a special case of the extended affinely adjustable robust counterpart—the splittingbased extended affinely adjustable robust counterpart—and illustrate both theoretically and computationally that the potential of the affinely adjustable robust counterpart method is well beyond the one presented in the literature. Similar to the affinely adjustable robust counterpart, our approach ends up with deterministic optimization formulations that are tractable and scalable to multistage problems.
Robust allocation of a defensive budget considering an attacker’s private information
 Risk Analysis
"... Attackers ’ private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker’s attributes. However, terrorists ’ goals may be unknown ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
Attackers ’ private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker’s attributes. However, terrorists ’ goals may be unknown to the defender, necessitating robust decisions by the defender. This article develops a robustoptimization gametheoretical model for identifying optimal defense resource allocation strategies for a rational defender facing a strategic attacker while the attacker’s valuation of targets, being the most critical attribute of the attacker, is unknown but belongs to bounded distributionfree intervals. To our best knowledge, no previous research has applied robust optimization in homeland security resource allocation when uncertainty is defined in bounded distributionfree intervals. The key features of our model include (1) modeling uncertainty in attackers ’ attributes, where uncertainty is characterized by bounded intervals; (2) finding the robustoptimization equilibrium for the defender using concepts dealing with budget of uncertainty and price of robustness; and (3) applying the proposed model to real data. KEY WORDS: Defenderattacker game; defense resource allocation; private information; robust optimization
A General RobustOptimization Formulation for Nonlinear Programming
 J. Optim. Theory Appl
, 2004
"... Most research in robust optimization has so far been focused on inequalityonly, convex conic programming with simple linear models for uncertain parameters. ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Most research in robust optimization has so far been focused on inequalityonly, convex conic programming with simple linear models for uncertain parameters.
Robust Portfolio Management
, 2004
"... In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the e#ect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints s ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the e#ect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, limits on cash exposure, etc. The optimal portfolios are computed by solving secondorder cone programs. Since the complexity of solving a secondorder cone program is comparable to that of solving a convex quadratic program, it follows that the e#ort required to compute the optimal robust portfolio is comparable to that of computing the Markowitz optimal portfolio. We report on the performance of our robust strategies in tracking the S&P 500 index over 19942003. We find that our robust strategy is able to track the index with a significantly smaller number of assets than a nonrobust meanvariance index tracking strategy. We propose a simple strategy for managing the cost of the robust index tracking strategy in markets with transaction costs. Our computational results also suggest that the robust active portfolio management strategy significantly outperforms the S&P 500 index without a significant increase in volatility. 1
Explicit reformulations of robust optimization problens with general uncertainty sets
 SIAM J. Optim
"... Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explici ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets defined by convex homogeneous functions. Our results provide a unified treatment of many situations that have been investigated in the literature, and are applicable to a wider range of problems and more complicated uncertainty sets than those considered before. The analysis in this paper makes it possible to use existing continuous optimization algorithms to solve more complicated robust optimization problems. The analysis also shows how the structure of the resulting reformulation of the robust counterpart depends both on the structure of the original nominal optimization problem and on the structure of the uncertainty set. Key words. Robust optimization, data uncertainty, mathematical programming, homogeneous functions, convex analysis AMS subject classifications. 90C30, 90C15, 90C34, 90C25, 90C05.
Learning heuristic functions through approximate linear programming
 International Conference on Automated Planning and Scheduling (ICAPS
, 2008
"... Planning problems are often formulated as heuristic search. The choice of the heuristic function plays a significant role in the performance of planning systems, but a good heuristic is not always available. We propose a new approach to learning heuristic functions from previously solved problem ins ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Planning problems are often formulated as heuristic search. The choice of the heuristic function plays a significant role in the performance of planning systems, but a good heuristic is not always available. We propose a new approach to learning heuristic functions from previously solved problem instances in a given domain. Our approach is based on approximate linear programming, commonly used in reinforcement learning. We show that our approach can be used effectively to learn admissible heuristic estimates and provide an analysis of the accuracy of the heuristic. When applied to common heuristic search problems, this approach reliably produces good heuristic functions.