Results 11  20
of
67
Cuts for mixed 01 conic programming
, 2005
"... In this we paper we study techniques for generating valid convex constraints for mixed 01 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 01 linear programs, such as the Gomory cuts, the liftandproject cuts, and cuts from other hierarchies of ti ..."
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Cited by 27 (0 self)
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In this we paper we study techniques for generating valid convex constraints for mixed 01 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 01 linear programs, such as the Gomory cuts, the liftandproject cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 01 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 01 conic programs have interesting implications for comparing the semidefinite programming and the linear programming relaxations of combinatorial optimization problems, e.g. we show that all the subtour elimination inequalities for the traveling salesman problem are rank1 Gomory cuts with respect to a single semidefinite constraint. We also include results from our preliminary computational experiments with these cuts.
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
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Cited by 24 (5 self)
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In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
Robust Filtering for DiscreteTime Systems with Bounded Noise and Parametric Uncertainty
 IEEE Trans. Aut. Control
, 2001
"... This paper presents a new approach to finitehorizon guaranteed state prediction for discretetime systems affected by bounded noise and unknownbutbounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the statespace matrices on the uncertain parameters. The main re ..."
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Cited by 23 (3 self)
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This paper presents a new approach to finitehorizon guaranteed state prediction for discretetime systems affected by bounded noise and unknownbutbounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the statespace matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interiorpoint methods for convex optimization. With n states, l uncertain parameters appearing linearly in the statespace matrices, with rankone matrix coefficients, the worstcase complexity grows as O(l(n + l) 3:5 ). With unstructured uncertainty in all system matrices, the worstcase complexity reduces to O(n 3:5 ).
Robust Convex Quadratically Constrained Programs
 Mathematical Programming
, 2002
"... In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by BenTal and Nemirovski [4]. Unlike [4], our focus in this paper is to identify uncertainty structures that allow the corresponding robust quadratically constrained p ..."
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Cited by 18 (2 self)
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In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by BenTal and Nemirovski [4]. Unlike [4], our focus in this paper is to identify uncertainty structures that allow the corresponding robust quadratically constrained programs to be reformulated as secondorder cone programs. We propose three classes of uncertainty sets that satisfy this criterion and present examples where these classes of uncertainty sets are natural. 1 Problem formulation A generic quadratically constrained program (QCP) is defined as follows.
Stochastic Algorithms for Exact and Approximate Feasibility of Robust LMIs
, 2001
"... In this note, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form ( 1) 0, where is the optimization variable and 1 is the uncertainty, which belongs to a given set 1. The proposed algorithms are based on uncertainty r ..."
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Cited by 17 (3 self)
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In this note, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form ( 1) 0, where is the optimization variable and 1 is the uncertainty, which belongs to a given set 1. The proposed algorithms are based on uncertainty randomization: the first algorithm finds a robust solution in a finite number of iterations with probability one, if a strong feasibility condition holds. In case no robust solution exists, the second algorithm computes an approximate solution which minimizes the expected value of a suitably selected feasibility indicator function. The theory is illustrated by examples of application to uncertain linear inequalities and quadratic stability of interval matrices.
Constructing uncertainty sets for robust linear optimization
, 2006
"... doi 10.1287/opre.1080.0646 ..."
Robust design of biological experiments
 In NIPS
, 2006
"... We address the problem of robust, computationallyefficient design of biological experiments. Classical optimal experiment design methods have not been widely adopted in biological practice, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model ar ..."
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Cited by 13 (0 self)
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We address the problem of robust, computationallyefficient design of biological experiments. Classical optimal experiment design methods have not been widely adopted in biological practice, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model are poor, and in part because of computational constraints. We present a method for robust experiment design based on a semidefinite programming relaxation. We present an application of this method to the design of experiments for a complex calcium signal transduction pathway, where we have found that the parameter estimates obtained from the robust design are better than those obtained from an “optimal ” design. 1
Distributionally robust optimization and its tractable approximations
 Operations Research
"... In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard techni ..."
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Cited by 13 (3 self)
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In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by firstly affinelyextending the set of primitive uncertainties to generate new linear decision rules of larger dimensions, and are therefore more flexible. Next, we develop new piecewiselinear decision rules which allow a more flexible reformulation of the original problem. The reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables. Finally, we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations. These bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds, and next integrating them into a combined bound that is better than each of the individual bounds.
Cuttingset methods for robust convex optimization with pessimizing oracles,” Optim
 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 10 (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. Key words. Robust optimization, cuttingset methods, semiinfinite programming, minimax optimization, games.
Ellipsoidal bounds for uncertain linear equations and dynamical systems
, 2003
"... In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. This formulat ..."
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Cited by 9 (0 self)
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In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. This formulation leads to convex optimization problems that can be essentially solved in O(n 3)—n being the size of unknown vector — by means of suitable interior point barrier methods, as well as to closed form results in some particular cases. We further show that the uncertain linear equations paradigm can be directly applied to various statebounding problems for dynamical systems subject to setvalued noise and model uncertainty.