A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are linear programs (LP), second order cone programs (SOCP), semidefini...
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A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are linear programs (LP), second order cone programs (SOCP), semidefinite problems (SDP), and copositive problems. We survey recent progress made in this area. In particular, we highlight the connections between nonconvex quadratic problems, binary quadratic problems, and copositive optimization. We review how tight bounds can be obtained by relaxing the copositivity constraint to semidefiniteness, and we discuss the effect that different modelling techniques have on the quality of the bounds. We also provide some new techniques for lifting linear constraints and show how these can be used for stable set and coloring relaxations.
Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this...
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Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.
We investigate relaxations for the maximum stable set problem based on the Lovasz numb theta(G) as an initial upper bound. We strengthen this relaxation by adding two classes of cutting planes, odd circuit and triangl...
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We investigate relaxations for the maximum stable set problem based on the Lovasz numb theta(G) as an initial upper bound. We strengthen this relaxation by adding two classes of cutting planes, odd circuit and triangle inequalities. We present computational results using this tighter model on many classes of graphs.
We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G = (V, E) and ...
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We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G = (V, E) and k numbers rho(1),..., rho(k). The goal is to partition V into k disjoint sets (bins) P-1,..., P-k satisfying vertical bar P-i vertical bar <= rho(i)vertical bar V vertical bar for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(root log vertical bar V vertical bar log k) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints vertical bar P-i vertical bar <= (5 + epsilon)rho(i)vertical bar V vertical bar. This algorithm is an improvement upon the O(log vertical bar V vertical bar)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and programming (ICALP 2014).
Localization through received signal strength (RSS) has attained a lot of interest across industries and research organization due to ease of use, high efficiency and low computation complexity;thus, it is widely used...
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Localization through received signal strength (RSS) has attained a lot of interest across industries and research organization due to ease of use, high efficiency and low computation complexity;thus, it is widely used in Wireless Sensor Networks (WSNs)-based applications. Existing localization model has been predominantly designed with known transmit power. Recently, few localization approaches have been modeled considering unknown transmit power employing non-convex least squared relative error (LSRE) measurement model. The LSRE optimization problem is solved through semidefinite programming (SDP) using semidefinite relaxation (SDR). However, LSRE-SDP suffers immensely under highly dynamic and noisy environment and induces high computation overhead in meeting convergence. In addressing the aforementioned problem, this paper presents Dynamic Noisy Measurement Aware Localization (DNMAL) model for WSNs using improved least square bounding model. The objective DNMAL is to measure target position by neglecting the collected through noisy (faulty) sensor device. The DNMAL aids in achieving optimal solution using improved least square bounding model through iterative process. The DNMAL is efficient in bounding unknown distribution because of presence of noisy sensor and significantly reduces localization error even with presence of extreme noise.
Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of...
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Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter's classification and semidefinite programming.
In this paper, we show that linear varieties of polynomials can be used to approximate linear varieties of the space of continuous functions. This property is important in applications where polynomial optimization is...
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In this paper, we show that linear varieties of polynomials can be used to approximate linear varieties of the space of continuous functions. This property is important in applications where polynomial optimization is used as it allows one to impose affine constraints on the decision variables with no loss of accuracy. In particular, construction of Lyapunov functionals for systems with delay is discussed.
This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We main...
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This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.
We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which...
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We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.
A hole in a flexible pavement is commonly formed due to several environmental impacts. With a continued overload traffic action, a collapse of the hole over the flexible pavement can potentially occur resulting in a p...
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A hole in a flexible pavement is commonly formed due to several environmental impacts. With a continued overload traffic action, a collapse of the hole over the flexible pavement can potentially occur resulting in a pothole on a road surface. Solutions of trapdoor problems are useful for predicting the failure of the hole taking place below the flexible pavement subjected to the overload traffic. In this paper, the collapse pressure on flexible pavements over rectangular trapdoors in homogeneous clay is investigated by a three-dimensional lower bound finite element limit analysis using semidefinite programming. Results of the present study are verified against the existing solutions for the cases of plane strain trapdoors. New lower bound solutions of the problem are numerically derived as functions of cover-depth ratios and aspect ratios of rectangular trapdoors while associated failure mechanisms are discussed and compared. Approximate algebraic equations for stability numbers of rectangular trapdoors are also presented.
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