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2,272
A Stochastic Semidefinite Programming Approach to Side Chain Positioning
, 2008
"... The sidechain positioning (SCP) problems are very important subproblems in computational molecular biology. Basically they can be characterized as optimization problems. For a given backbone chain and some residues with rotamers[Dunbrack and Karplus, 1993], solving SCP is to minimize the total ener ..."
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The sidechain positioning (SCP) problems are very important subproblems in computational molecular biology. Basically they can be characterized as optimization problems. For a given backbone chain and some residues with rotamers[Dunbrack and Karplus, 1993], solving SCP is to minimize the total energy of this protein, i.e. to find a
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Semidefinite Programming Relaxations for Semialgebraic Problems
, 2001
"... A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The mai ..."
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Cited by 365 (23 self)
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. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques provide a constructive approach for finding bounded degree solutions to the Positivstellensatz
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 532 (5 self)
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stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient
An InteriorPoint Method for Semidefinite Programming
, 2005
"... We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other appli ..."
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Cited by 254 (19 self)
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We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other
Stochastic Approximation Approach to Stochastic Programming
"... In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of th ..."
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Cited by 267 (20 self)
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of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA) methods. Both approaches, the SA and SAA methods, have a long history. Current opinion is that the SAA method can efficiently
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.
A Spectral Bundle Method for Semidefinite Programming
 SIAM JOURNAL ON OPTIMIZATION
, 1997
"... A central drawback of primaldual interior point methods for semidefinite programs is their lack of ability to exploit problem structure in cost and coefficient matrices. This restricts applicability to problems of small dimension. Typically semidefinite relaxations arising in combinatorial applica ..."
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Cited by 171 (7 self)
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A central drawback of primaldual interior point methods for semidefinite programs is their lack of ability to exploit problem structure in cost and coefficient matrices. This restricts applicability to problems of small dimension. Typically semidefinite relaxations arising in combinatorial
The linear programming approach to approximate dynamic programming
 Operations Research
, 2001
"... The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear ..."
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Cited by 225 (16 self)
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The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear
Robust Solutions To Uncertain Semidefinite Programs
 SIAM J. OPTIMIZATION
, 1998
"... In this paper we consider semidefinite programs (SDPs) whose data depend on some unknown but bounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible value ..."
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Cited by 114 (8 self)
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In this paper we consider semidefinite programs (SDPs) whose data depend on some unknown but bounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible value
Results 1  10
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2,272