Low-delay nonuniform oversampled filterbanks have a good applicability in real-time audio applications. An appealing trade-off between complexity and frequency division is obtained by using filterbanks having uniform ...
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Low-delay nonuniform oversampled filterbanks have a good applicability in real-time audio applications. An appealing trade-off between complexity and frequency division is obtained by using filterbanks having uniform sections generated by generalized DFT modulation, with transition filters between the uniform sections. We propose two methods for designing such filterbanks, with no restrictions on the widths of transition filters. The first method is iterative and each iteration consists of convex optimization problems. In the second, faster method, the transition filters are designed using a frequency sampling technique. We present an example of design showing the good results of the proposed methods. (C) 2008 Elsevier B.V. All rights reserved.
Weighted determinant maximization with linear matrix inequality constraints (maxdet-problem) is a generalization of the semidefinite programming. We give a polynomial-time complexity analysis for the path-following in...
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Weighted determinant maximization with linear matrix inequality constraints (maxdet-problem) is a generalization of the semidefinite programming. We give a polynomial-time complexity analysis for the path-following interior-point short-step and predictor-corrector methods for the maxdet-problem based on symmetric Newton equations for certain classes of scaling matrices.
For an ideal I subset of R[x] given by a set of generators, a new semidefinite characterization of its real radical I(V-R(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover, we propose an a...
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For an ideal I subset of R[x] given by a set of generators, a new semidefinite characterization of its real radical I(V-R(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover, we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V-R(I) as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Grobner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.
We analyze Brownian simulation methods for systems of partial differential equations coupled to convection-diffusion equations. In many situations the spatial correlation of Brownian noise can be viewed as a free para...
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We analyze Brownian simulation methods for systems of partial differential equations coupled to convection-diffusion equations. In many situations the spatial correlation of Brownian noise can be viewed as a free parameter. We formulate the choice of the noise correlation as an optimization problem for mean error minimization. In contrast to earlier work which was restricted to systems of finite dimensions, our formulation is performed in function space. We then provide an approximation theorem that reduces the problem into the solution of finite-dimensional semidefinite programming problems. Examples are given to illustrate our main results.
Here, we solve non-convex, variational problems given in the form min(u) I (u) = integral(1)(0) f (u' (x))dx s.t. u(0) = 0, u(1) = a, (1) where u is an element of (W-1,W-infinity(0,1))(k) and f : R-k -> R is a ...
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Here, we solve non-convex, variational problems given in the form min(u) I (u) = integral(1)(0) f (u' (x))dx s.t. u(0) = 0, u(1) = a, (1) where u is an element of (W-1,W-infinity(0,1))(k) and f : R-k -> R is a non-convex, coercive polynomial. To solve ( 1) we analyse the convex hull of the integrand at the point a, so that we can find vectors a(1),...,a(N) is an element of R-k and positive values lambda(1),...,lambda(N) satisfying the non-linear equation (1, a, f(c)(a)) = Sigma(N)(i=1)lambda(i)(1, a(i), f(a(i))). (2) Thus, we can calculate minimizers of (1) by following a proposal of Dacorogna in (Direct Methods in the Calculus of Variations. Springer, Heidelberg, 1989). Indeed, we can solve (2) by using a semidefinite program based on multidimensional moments.
Eigenvectors to the second smallest eigenvalue of the Laplace matrix of a graph, also known as Fiedler vectors, are the basic ingredient in spectral graph partitioning heuristics. Maximizing this second smallest eigen...
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Eigenvectors to the second smallest eigenvalue of the Laplace matrix of a graph, also known as Fiedler vectors, are the basic ingredient in spectral graph partitioning heuristics. Maximizing this second smallest eigenvalue over all nonnegative edge weightings with bounded total weight yields the absolute algebraic connectivity introduced by Fiedler, who proved tight connections of this value to the connectivity of the graph. Our objective is to gain a better understanding of the connections between separators and the eigenspace of this eigenvalue by studying the dual semidefinite optimization problem to the absolute algebraic connectivity. By exploiting optimality conditions we show that this problem is equivalent to finding an embedding of the n nodes of the graph in n-space so that their barycenter is the origin, the distance between adjacent nodes is bounded by one, and the nodes are spread as much as possible (the sum of the squared norms is maximized). For connected graphs we prove that, for any separator in the graph, at least one of the two separated node sets is embedded in the shadow (with the origin being the light source) of the convex hull of the separator. Furthermore, we show that there always exists an optimal embedding whose dimension is bounded by the tree width of the graph plus one.
We present a unifying framework to establish a lower bound on the number of semidefinite-programming-based lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinat...
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We present a unifying framework to establish a lower bound on the number of semidefinite-programming-based lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinatorial optimization problems. This framework is based on the maps which are commutative with the lift-and-project operators. Some special commutative maps were originally observed by Lovasz and Schrijver and have been used usually implicitly in the previous lower-bound analyses. In this paper, we formalize the lift-and-project commutative maps and propose a general framework for lower-bound analysis, in which we can recapture many of the previous lower-bound results on the lift-and-project ranks. (c) 2007 Elsevier B.V. All rights reserved.
It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization problem. Examples of conic constraints include semidefinite constraints and second order cone ...
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It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper, a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly feasible points in both the primal and dual spaces can be defined. A second benefit of the modification is an improvement in the complexity analysis of conic cutting surface algorithms. Complexity results for conic cutting surface algorithms proved to date have depended on a condition number of the added constraints. The proposed modification of the constraints leads to a stronger result, with the convergence of the resulting algorithm not dependent on the condition number.
Many combinatorial optimization problems can be modelled as polynomial-programming problems in binary variables that are all 0-1 or 1. A sufficient condition under which a common method for obtaining semidefinite-prog...
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Many combinatorial optimization problems can be modelled as polynomial-programming problems in binary variables that are all 0-1 or 1. A sufficient condition under which a common method for obtaining semidefinite-programming relaxations of the two models of the same problem gives equivalent relaxations is established. (C) 2007 Elsevier B.V. All rights reserved.
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample ...
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Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight conditional independence relationships between the sample variables. We first formulate a convex relaxation of this combinatorial problem, we then detail two efficient first-order algorithms with low memory requirements to solve large-scale, dense problem instances.
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