Results 1  10
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110
Distributionally Robust Optimization under Moment Uncertainty with Application to DataDriven Problems
"... Stochastic programs can effectively describe the decisionmaking problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random param ..."
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Cited by 60 (4 self)
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Stochastic programs can effectively describe the decisionmaking problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model describing one’s uncertainty in both the distribution’s form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance). We demonstrate that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently. Furthermore, by deriving new confidence regions for the mean and covariance of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. This is confirmed in a practical example of portfolio selection, where our framework leads to better performing policies on the “true” distribution underlying the daily return of assets.
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 ..."
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Cited by 17 (5 self)
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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.
On the Power of Robust Solutions in TwoStage Stochastic and Adaptive Optimization Problems
"... informs doi 10.1287/moor.1090.0440 ..."
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Robust power allocation for energyefficient locationaware networks
 IEEE/ACM Trans. Netw
"... Abstract—In wireless locationaware networks, mobile nodes (agents) typically obtain their positions using the range measurements to the nodes with known positions. Transmit power allocation not only affects network lifetime and throughput, but also determines localization accuracy. In this paper, ..."
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Cited by 11 (4 self)
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Abstract—In wireless locationaware networks, mobile nodes (agents) typically obtain their positions using the range measurements to the nodes with known positions. Transmit power allocation not only affects network lifetime and throughput, but also determines localization accuracy. In this paper, we present an optimization framework for robust power allocation in network localization with imperfect knowledge of network parameters. In particular, we formulate power allocation problems to minimize localization errors for a given power budget and show that such formulations can be solved via conic programming. Moreover, we design a distributed power allocation algorithm that allows parallel computation among agents. The simulation results show that the proposed schemes significantly outperform uniform power allocation, and the robust schemes outperform their nonrobust counterparts when the network parameters are subject to uncertainty. Index Terms—Localization, resource allocation, robust optimization, secondorder conic programming (SOCP), semidefinite programming (SDP), wireless networks. I.
Power optimization for network localization
 IEEE/ACM Trans. on Networking
, 2014
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Thresholded Covering Algorithms for Robust and MaxMin Optimization
, 2009
"... The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worstcase cost (summed over both days) is minimized? For example, in a set co ..."
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Cited by 9 (4 self)
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The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worstcase cost (summed over both days) is minimized? For example, in a set cover instance, if any one of the () n k subsets of the universe that have size k may appear tomorrow, what is a good course of action? Feige et al. [FJMM07], and later, Khandekar et al. [KKMS08], considered this krobust model where the possible outcomes tomorrow are given by all demandsubsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for krobust problems: having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold (which is ≈ Opt/k), augment the anticipatory solution to cover this demand as well, and repeat. In this paper we show that this template gives us approximation algorithms for krobust versions of Steiner tree and set
A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization
"... In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed in ..."
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Cited by 8 (5 self)
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In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multistage stochastic as well as the adaptive optimization problem. A finitely adaptable solution generalizes the notion of a static robust solution and specifies a small set of solutions for each stage and the solution policy implements the best solution from the given set depending on the realization of the uncertain parameters in past stages. Therefore, it is a tractable approximation to a fullyadaptable solution for the multistage problems. To the best of our knowledge, these are the first approximation results for the multistage problem in such generality. Moreover, the results and the proof techniques are quite general and also extend to include important constraints such as integrality and linear conic constraints.
Y.: Likelihood robust optimization for datadriven problems
, 2013
"... We consider the optimal decision making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown yet there is abundant historical data for it. In this paper, we propose a new type of distributionally robust optimization model which ..."
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Cited by 7 (0 self)
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We consider the optimal decision making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown yet there is abundant historical data for it. In this paper, we propose a new type of distributionally robust optimization model which we call the likelihood robust optimization (LRO) for this class of problems. In contrast to most prior work on distributionally robust optimization which focus on certain parameters (e.g., mean, variance etc) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of maximizing the expected value of the objective function under the worstcase distribution in that set. Our model can avoid the overconservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present detailed statistical analysis of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance. 1
Tractable stochastic analysis in high dimensions via robust optimization
 MATH. PROGRAM., SER. B
, 2012
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Robust distributed linear programming,”
 IEEE Transactions on Automatic Control,
, 2013
"... AbstractThis paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show that the resulting continuoustime saddlepoint algor ..."
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Cited by 6 (5 self)
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AbstractThis paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show that the resulting continuoustime saddlepoint algorithm is provably correct but, in general, not distributed because of a global parameter associated with the nonsmooth exact penalty function employed to encode the inequality constraints of the linear program. This motivates the design of a discontinuous saddlepoint dynamics that, while enjoying the same convergence guarantees, is fully distributed and scalable with the dimension of the solution vector. We also characterize the robustness against disturbances and link failures of the proposed dynamics. Specifically, we show that it is integralinputtostate stable but not inputtostate stable. The latter fact is a consequence of a more general result, that we also establish, which states that no algorithmic solution for linear programming is inputtostate stable when uncertainty in the problem data affects the dynamics as a disturbance. Our results allow us to establish the resilience of the proposed distributed dynamics to disturbances of finite variation and recurrently disconnected communication among the agents. Simulations in an optimal control application illustrate the results.