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Robust convex optimization
 Mathematics of Operations Research
, 1998
"... We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we la ..."
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Cited by 416 (21 self)
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We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we
Adjustable robust solutions of uncertain linear programs
, 2004
"... We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (“nonadjustable variables”), while the other part are variables that can be chosen after the realization ..."
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Cited by 370 (12 self)
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cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multistage inventory management problem.
The Computational Complexity of Propositional STRIPS Planning
 Artificial Intelligence
, 1994
"... I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation ..."
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Cited by 363 (3 self)
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in pre and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACEcomplete to determine if a given planning instance has any solutions. Extremely severe restrictions on both
Tractable conservative Constraint Satisfaction Problems
"... In a constraint satisfaction problem (CSP) the aim is to find an assignment of values to a given set of variables, subject to specified constraints. The CSP is known to be NPcomplete in general. However, certain restrictions on the form of the allowed constraints can lead to problems solvable in po ..."
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Cited by 118 (13 self)
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constraint languages that give rise to CSP classes solvable in polynomial time. In particular, this result allows us to obtain a complete description of those (directed) graphs H for which the LIST HCOLORING problem is polynomial time solvable.
Tractable approximations of robust conic optimization problems
, 2006
"... In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NPha ..."
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Cited by 70 (14 self)
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hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs
An Approximate MaxFlow MinCut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms
, 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf halfunits of commodity (uv) from u to v and f halfunits of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
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Cited by 246 (12 self)
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9 task provided that the capacity of each cut exceeds the demand across the cut by a b(log n) factor. The condition on cuts is required in the worst case, and is trivially within a i(log n) factor of optimal for any flow problem. The result is of interest because it can be used to construct
Robust discrete optimization and network flows
 Mathematical Programming Series B
, 2003
"... We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data ..."
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Cited by 194 (27 self)
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We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data
Tractable optimal competitive scheduling
 Proc. 16th International Conference on Automated Planning and Scheduling (ICAPS
, 2006
"... In this paper we describe the problem of Optimal Competitive Scheduling, which consists of activities that compete for a shared resource. The objective is to choose a subset of activities to schedule, sequence them, and decide how much time they are allowed, in such a way that temporal and resourc ..."
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Cited by 1 (0 self)
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. The first class of tractable OCS problems arises due to limitations on the objective function that permit casting the problem as a Linear Program; with one additional assumption on activity feasibility windows, we identify a problem class where an optimal activity ordering can be found in polynomial time
Continuous problems: optimality, complexity, tractability
, 2013
"... Since a digital computer is able to store and manipulate only with finitely many real numbers, most computational problems of continuous mathematics can only be solved approximately using partial information. A branch of computational mathematics that studies the inherent difficulty of continuous pr ..."
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Since a digital computer is able to store and manipulate only with finitely many real numbers, most computational problems of continuous mathematics can only be solved approximately using partial information. A branch of computational mathematics that studies the inherent difficulty of continuous
NearOptimal Plans, Tractability, and Reactivity
 In Proc. of KR 94
, 1994
"... Many planning problems have recently been shown to be inherently intractable. For example, finding the shortest plan in the blocksworld domain is NPhard, and so is planning in even some of the most limited STRIPSstyle planning formalisms. We explore the question as to what extent these negative res ..."
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Cited by 35 (2 self)
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Many planning problems have recently been shown to be inherently intractable. For example, finding the shortest plan in the blocksworld domain is NPhard, and so is planning in even some of the most limited STRIPSstyle planning formalisms. We explore the question as to what extent these negative
Results 1  10
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1,748