The Experts below are selected from a list of 21189 Experts worldwide ranked by ideXlab platform
Soondal Park - One of the best experts on this subject based on the ideXlab platform.
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An [epsilon]-sensitivity analysis for Semidefinite Programming
European Journal of Operational Research, 2005Co-Authors: Soondal ParkAbstract:Abstract We extend the concept of ϵ -sensitivity analysis developed for linear Programming to that for Semidefinite Programming. First, the notion of ϵ -optimality for a given Semidefinite Programming problem is defined, and then a generic ϵ -sensitivity analysis for Semidefinite Programming is introduced. Based on the definitions, we develop an implementation of the generic ϵ -sensitivity analysis under perturbations of either the cost parameters or the right-hand side.
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An ϵ-sensitivity analysis for Semidefinite Programming
European Journal of Operational Research, 2005Co-Authors: Sungmook Lim, Sangwook Lee, Soondal ParkAbstract:Abstract We extend the concept of ϵ -sensitivity analysis developed for linear Programming to that for Semidefinite Programming. First, the notion of ϵ -optimality for a given Semidefinite Programming problem is defined, and then a generic ϵ -sensitivity analysis for Semidefinite Programming is introduced. Based on the definitions, we develop an implementation of the generic ϵ -sensitivity analysis under perturbations of either the cost parameters or the right-hand side.
Bruce Hajek - One of the best experts on this subject based on the ideXlab platform.
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achieving exact cluster recovery threshold via Semidefinite Programming
International Symposium on Information Theory, 2015Co-Authors: Bruce HajekAbstract:The binary symmetric stochastic block model deals with a random graph of n vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability p within clusters and q across clusters. In the asymptotic regime of p = a log n/n and q = b log n/n for fixed a, b and n → ∞, we show that the Semidefinite Programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe et al. [1]. Furthermore, we show that the Semidefinite Programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to n.
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achieving exact cluster recovery threshold via Semidefinite Programming
arXiv: Machine Learning, 2014Co-Authors: Bruce HajekAbstract:The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across clusters. In the asymptotic regime of $p=a \log n/n$ and $q=b \log n/n$ for fixed $a,b$ and $n \to \infty$, we show that the Semidefinite Programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe et al. \cite{Abbe14}. Furthermore, we show that the Semidefinite Programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to $n$.
Gao Leif - One of the best experts on this subject based on the ideXlab platform.
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A Nonmonotonic Trust Region Algorithm for Solving Semidefinite Programming
Computer Engineering, 2013Co-Authors: Gao LeifAbstract:A nonmonotonic trust region algorithm for solving Semidefinite Programming(SDP) is proposed in this paper.The equivalent smoothing equations of the optimal condition are obtained by exploiting the Fischer-Burmeister function that is extended to the matrix domain,and the center of the path of SDP is rewritten.The algorithm makes full use of first-order gradient information of the current iteration point to solve the trust region subproblem,and a new trust region radius selection mechanism is proposed.Simulation results show that the algorithm runs faster than the classical interior point algorithm for general scale Semidefinite Programming problems(n,m≤30),for large-scale Semidefinite Programming problem(n,m30) the algorithm is suitable for handling Norm min,Lovasz these two kinds of problems.
Shuzhong Zhang - One of the best experts on this subject based on the ideXlab platform.
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Symmetric primal-dual path-following algorithms for Semidefinite Programming
Applied Numerical Mathematics, 1999Co-Authors: J.f. Sturm, Shuzhong ZhangAbstract:We propose a framework for developing and analyzing primal-dual interior point algorithms for Semidefinite Programming. This framework is an extension of the v-space approach that was developed by Kojima et al. (1991) for linear complementarity problems. The extension to Semidefinite Programming allows us to interpret Nesterov-Todd type directions (Nesterov and Todd 1995, 1997) as Newton search directions. Our approach does not involve any barrier function. Several primal-dual path-following algorithms for Semidefinite Programming are analyzed. The treatment of these algorithms for Semidefinite Programming in our setting bears great similarity to the linear Programming case.
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Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming
1996Co-Authors: Arjan Berkelaar, J.f. Sturm, Shuzhong ZhangAbstract:textabstractIn this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to Semidefinite Programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to Semidefinite Programming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for Semidefinite Programming, our algorithm enjoys the lowest computational complexity.
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Symmetric primal-dual path following algorithms for Semidefinite Programming
1995Co-Authors: J.f. Sturm, Shuzhong ZhangAbstract:In this paper a symmetric primal-dual transformation for positive Semidefinite Programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear Programming, existence of such a primal-dual transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newton search directions for primal-dual path-following algorithms for Semidefinite Programming. In particular, we generalize: (1) the short step path following algorithm, (2) the predictor-corrector algorithm and (3) the largest step algorithm to Semidefinite Programming. It is shown that these algorithms require at most [TeX: ${\\cal O}(\\sqrt{n}\\mid \\log \\epsilon \\mid ) $] main iterations for computing an [TeX: $\\epsilon $]-optimal solution.
George C. Verghese - One of the best experts on this subject based on the ideXlab platform.
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Designing optimal quantum detectors via Semidefinite Programming
IEEE Transactions on Information Theory, 2003Co-Authors: Yonina C. Eldar, Alexandre Megretski, George C. VergheseAbstract:We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a Semidefinite Programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) Semidefinite program. By exploiting the many well-known algorithms for solving Semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the Semidefinite Programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.
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designing optimal quantum detectors via Semidefinite Programming
arXiv: Quantum Physics, 2002Co-Authors: Yonina C. Eldar, Alexandre Megretski, George C. VergheseAbstract:We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a Semidefinite Programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) Semidefinite program followed by the solution of a set of linear equations or, at worst, a standard linear Programming problem. By exploiting the many well-known algorithms for solving Semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time. Using the Semidefinite Programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.
