We focus on the analysis of homogeneous, non-convex, non-local variational principles given in the general form: min(u) integral integral(integral x integral) W (u'(x), u' (y)) dx dy where W can be expressed a...
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We focus on the analysis of homogeneous, non-convex, non-local variational principles given in the general form: min(u) integral integral(integral x integral) W (u'(x), u' (y)) dx dy where W can be expressed as a polynomial. This work. extends previous result of Pedregal (1997) [19] by using moments of parametrized measures to transform the generalized form of the problem in terms of Young measures into a more convenient mathematical program with quadratic and conic structure. (C) 2011 Elsevier Inc. All rights reserved.
When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in th...
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When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559-1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138-1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992]. (C) 2011 Elsevier B.V. All rights reserved.
We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arb...
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We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n;this is based on a result of de Klerk et al. (Math Program, 2006) about the regular *-representation for matrix *-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859-2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n(7)) variables and thus seems out of reach for interesting values of n, Schrijver's bound can be computed via a semidefinite program of size O(n(3)), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver's bound with the same computational complexity.
Network datasets have become ubiquitous in many fields of study in recent years. In this paper we investigate a problem with applicability to a wide variety of domains - detecting small, anomalous subgraphs in a backg...
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ISBN:
(纸本)9781457705700
Network datasets have become ubiquitous in many fields of study in recent years. In this paper we investigate a problem with applicability to a wide variety of domains - detecting small, anomalous subgraphs in a background graph. We characterize the anomaly in a subgraph via the well-known notion of network modularity, and we show that the optimization problem formulation resulting from our setup is very similar to a recently introduced technique in statistics called Sparse Principal Component Analysis (Sparse PCA), which is an extension of the classical PCA algorithm. The exact version of our problem formulation is a hard combinatorial optimization problem, so we consider a recently introduced semidefinite programming relaxation of the Sparse PCA problem. We show via results on simulated data that the technique is very promising.
We study Lovász and Schrijver's hieararchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single app...
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We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interi...
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We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R-2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub-networks in the input network.
In this paper, we first demonstrate that positive semidefiniteness of a large well-structured sparse symmetric matrix can be represented via positive semidefiniteness of a bunch of smaller matrices linked, in a linear...
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In this paper, we first demonstrate that positive semidefiniteness of a large well-structured sparse symmetric matrix can be represented via positive semidefiniteness of a bunch of smaller matrices linked, in a linear fashion, to the matrix. We derive also the "dual counterpart" of the outlined representation, which expresses the possibility of positive semidefinite completion of a well-structured partially defined symmetric matrix in terms of positive semidefiniteness of a specific bunch of fully defined submatrices of the matrix. Using the representations, we then reformulate well-structured large-scale semidefinite problems into smooth convex-concave saddle point problems, which can be solved by a Prox-method developed in [6] with efficiency O(epsilon(-1)). Implementations and some numerical results for large-scale Lovsz capacity and MAXCUT problems are finally presented.
Given a code C is an element of F-2(n) and a word c is an element of C, a witness of c is a subset W subset of {, 1 ... , n} of coordinate positions such that c differs from any other codeword c' is an element of ...
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ISBN:
(纸本)9781457705953
Given a code C is an element of F-2(n) and a word c is an element of C, a witness of c is a subset W subset of {, 1 ... , n} of coordinate positions such that c differs from any other codeword c' is an element of C on the indices in W. If any codeword posseses a witness of given length w, C is called a w-witness code. This paper gives new constructions of large w-witness codes and proves with a numerical method that their sizes are maximal for certain values of n and w. Our technique is in the spirit of Delsarte's linear programming bound on the size of classical codes and relies on the Lovasz theta number, semidefinite programming, and reduction through symmetry.
When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in th...
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When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559-1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138-1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992]. (C) 2011 Elsevier B.V. All rights reserved.
Solving Fastest Distributed Consensus (FDC) averaging problem over sensor networks with different topologies has received some attention recently and one of the well known topologies in this issue is star-mesh hybrid ...
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ISBN:
(纸本)9781612842332
Solving Fastest Distributed Consensus (FDC) averaging problem over sensor networks with different topologies has received some attention recently and one of the well known topologies in this issue is star-mesh hybrid topology. Here in this work we present analytical solution for the problem of FDC algorithm by means of stratification and semidefinite programming, for the Star-Mesh Hybrid network with K-partite core (SMHK) which has rich symmetric properties. Also the variations of asymptotic and per step convergence rate of SMHK network versus its topological parameters have been studied numerically.
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