This paper is devoted to tackling the control problem for a class of discrete-time stochastic systems with randomly occurring sensor saturations. The considered sensor saturation phenomenon is assumed to occur in a ra...
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This paper is devoted to tackling the control problem for a class of discrete-time stochastic systems with randomly occurring sensor saturations. The considered sensor saturation phenomenon is assumed to occur in a random way based on the time-varying Bernoulli distribution with measurable probability in real time. The aim of the paper is to design a nonfragile gain-scheduled controller with probability-dependent gains which can be achieved by solving a convex optimization problem via semidefinite programming method. Subsequently, a new kind of probability-dependent Lyapunov functional is proposed in order to derive the controller with less conservatism. Finally, an illustrative example will demonstrate the effectiveness of our designed procedures.
We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from financ...
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We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method.
In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient contro...
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In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology.
A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback proble...
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A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).
Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communicati...
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Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. In this paper, we give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data;(ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in Studzinski et al. (Sci Rep 7(1):1-11, 2017) and Mozrzymas et al. (N J Phys 20(5):053006, 2018) using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this paper.
We make an experimental comparison of methods for computing the numerical radius of an n x n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable a...
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We make an experimental comparison of methods for computing the numerical radius of an n x n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in n(2) + 1 real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.
Fundamental matrix estimation is a central problem in computer vision and forms the basis of tasks such as stereo imaging and structure from motion. A new method for the estimation of the fundamental matrix from point...
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ISBN:
(纸本)9781424421138
Fundamental matrix estimation is a central problem in computer vision and forms the basis of tasks such as stereo imaging and structure from motion. A new method for the estimation of the fundamental matrix from point correspondences is presented. The minimization of an objective function closer to the geometric distance is performed based L. minimization framework. The fundamental matrix is optimally computed with taking into account the rank-two constraint, and the method is no need for normalization of the image coordinates. It is shown how this nonlinearly estimating the fundamental matrix can be solved avoiding local minima by using semidefinite programming. Experiments on real images show that this method provides a more accurate estimate of the fundamental matrix and superior to previous approaches.
Based on recent progress on moment problems, semidefinite optimization approach is proposed for estimating upper and lower bounds on linear functionals defined on solutions of linear integral equations with smooth ker...
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Based on recent progress on moment problems, semidefinite optimization approach is proposed for estimating upper and lower bounds on linear functionals defined on solutions of linear integral equations with smooth kernels. The approach is also suitable for linear integrodifferential equations with smooth kernels. Firstly, the primal problem with smooth kernel is converted to a series of approximative problems with Taylor polynomials obtained by expanding the smooth kernel. Secondly, two semidefinite programs (SDPs) are constructed for every approximative problem. Thirdly, upper and lower bounds on related functionals are gotten by applying SeDuMi 1.1R3 to solve the two SDPs. Finally, upper and lower bounds series obtained by solving two SDPs, respectively infinitely approach the exact value of discussed functional as approximative order of the smooth kernel increases. Numerical results show that the proposed approach is effective for the discussed problems.
It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparable in dominance order. The only excep...
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It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparable in dominance order. The only exception is the case of homogeneous symmetric functions where it is only known that dominance of the partitions implies nonnegativity of the corresponding difference of symmetric functions. It was conjectured by Cuttler, Greene, and Skandera in 2011 that the converse also holds, as in the cases of the monomial, elementary, power-sum, and Schur bases. In this paper we provide a counterexample, showing that homogeneous symmetric functions break the pattern. We use semidefinite programming to find an explicit sums of squares decomposition of the polynomial H-44 - H-521 as a sum of 41 squares. This rational certificate of nonnegativity disproves the conjecture, since a polynomial which is a sum of squares cannot be negative, and since the partitions 44 and 521 are incomparable in dominance order. (C) 2020 Elsevier B.V. All rights reserved.
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