In this paper we propose a novel finite-horizon, discrete-time, time-varying filtering method based on the robust semidefinite programming (SDP) technique. The proposed method provides robust performance in the presen...
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In this paper we propose a novel finite-horizon, discrete-time, time-varying filtering method based on the robust semidefinite programming (SDP) technique. The proposed method provides robust performance in the presence of norm-bounded parameter uncertainties in the system model. The robust performance of the proposed method is achieved by minimizing an upper bound on the worst-case variance of the estimation error for all admissible systems. Our method is recursive and computationally efficient. In our simulations, the new method provides superior performance to some of the existing robust filtering approaches. In particular, when applied to the problem of target tracking, the new method has led to a significant improvement in tracking performance. Our work shows that the robust SDP technique and the interior point algorithms can bring substantial benefits to practically important engineering problems.
In this paper we present several recent approaches for solving the Quadratic Assignment Problem (QAP). We first recall several semidefinite relaxations of QAP, and then present new QAP relaxations based on copositive ...
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ISBN:
(纸本)9616165208
In this paper we present several recent approaches for solving the Quadratic Assignment Problem (QAP). We first recall several semidefinite relaxations of QAP, and then present new QAP relaxations based on copositive programming. We discuss on the strength of the new relaxations and compare them with SDP ones.
In this paper, we explore the following question. Given a trigonometric polynomial q(z(1,). . ., z(d)) of several variables that is non-negative on the d-torus, how does one best approximate q with a (possibly outer) ...
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In this paper, we explore the following question. Given a trigonometric polynomial q(z(1,). . ., z(d)) of several variables that is non-negative on the d-torus, how does one best approximate q with a (possibly outer) single modulus square? Our answer will lie in the notion of an outer component, which coincides with the outer factor in the case of one variable. The outer component may be computed numerically using semidefinite programming. We shall derive some properties of outer components, as well as pose some open problems. (c) 2004 Elsevier Inc. All rights reserved.
A semidefinite program (SDP) is an optimization problem over n x n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknow...
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ISBN:
(纸本)3540435913
A semidefinite program (SDP) is an optimization problem over n x n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solving SDP's require O(n(3)) operations per iteration. We introduce subspace algorithms that greatly reduce the cost os solving large-scale SDP's. We apply these algorithms to SDP approximations of graph partitioning problems. We numerically compare our new algorithm with a standard semidefinite programming algorithm and show that our subspace algorithm performs better.
In this paper, we explore the following question. Given a trigonometric polynomial q(z(1,). . ., z(d)) of several variables that is non-negative on the d-torus, how does one best approximate q with a (possibly outer) ...
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In this paper, we explore the following question. Given a trigonometric polynomial q(z(1,). . ., z(d)) of several variables that is non-negative on the d-torus, how does one best approximate q with a (possibly outer) single modulus square? Our answer will lie in the notion of an outer component, which coincides with the outer factor in the case of one variable. The outer component may be computed numerically using semidefinite programming. We shall derive some properties of outer components, as well as pose some open problems. (c) 2004 Elsevier Inc. All rights reserved.
作者：
Halická, MComenius Univ
Fac Math Phys & Informat Dept Appl Math Bratislava 84248 Slovakia
In this paper we study the limiting behavior of the central path for semidefinite programming (SDP). We show that the central path is an analytic function of the barrier parameter even at the limit point, provided tha...
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In this paper we study the limiting behavior of the central path for semidefinite programming (SDP). We show that the central path is an analytic function of the barrier parameter even at the limit point, provided that the semidefinite program has a strictly complementary solution. A consequence of this property is that the derivatives - of any order of the central path have finite limits as the barrier parameter goes to zero. (C) 2002 Elsevier Science B.V. All rights reserved.
We consider the set g consisting of graphs of fixed order and weighted edges. The vertex set of graphs in g will correspond to point masses and the weight for an edge between two vertices is a functional of the distan...
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ISBN:
(纸本)0780390989
We consider the set g consisting of graphs of fixed order and weighted edges. The vertex set of graphs in g will correspond to point masses and the weight for an edge between two vertices is a functional of the distance between them. We pose the problem of finding the best vertex positional configuration in the presence of an additional proximity constraint, in the sense that, the second smallest eigenvalue of the corresponding graph Laplacian is maximized. In many recent applications of algebraic graph theory in systems and control, the second smallest eigenvalue of Laplacian has emerged as a critical parameter that influences the stability and robustness properties of dynamic systems that operate over an information network. Our motivation in the present work is to "assign" this Laplacian eigenvalue when relative positions of various elements dictate the interconnection of the underlying weighted graph. In this venue one would then he able to "synthesize" information graphs that have desirable system theoretic properties.
We describe an optimization method to approximate the arrival rate of data such as e-mail messages, website visits, changes to databases, and changes to websites mirrored by other servers. We model these arrival rates...
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ISBN:
(纸本)0780392329
We describe an optimization method to approximate the arrival rate of data such as e-mail messages, website visits, changes to databases, and changes to websites mirrored by other servers. We model these arrival rates as non-homogeneous Poisson process based on observed arrival data. We estimate the arrival function by cubic splines using the maximum likelihood principle. A critical feature of the model is that the splines are constrained to be everywhere nonnegative. We formulate this constraint using a characterization of nonnegative polynomials by positive semidefinite matrices. We also describe versions of our model that allow for periodic arrival rate functions and input data of limited precision. We formulate the estimation problem as a convex program related to semidefinite programming and solve it with a standard nonlinear optimization package called KNITRO. We present numerical results using both an actual record of e-mail arrivals over a period of sixty weeks, and artificially generated data sets. We also present a cross-validation procedure for determining an appropriate number of spline knots to model a set of arrival observations.
Adaptive estimation mechanism makes an important role in robot control since it is necessary to estimate changes of environment of a robot for the sake of adequate control. The least mean square (LMS) algorithm is one...
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ISBN:
(纸本)0780376579
Adaptive estimation mechanism makes an important role in robot control since it is necessary to estimate changes of environment of a robot for the sake of adequate control. The least mean square (LMS) algorithm is one of such adaptive estimation algorithms, and has been used as an effective and popular approach in signal processing because of its simple structure and low computational complexity. This paper proposes a design method for an LMS-type algorithm which is robust in some sense and converges faster than the conventional LMS algorithms. By means of recent robust control theory, the design problem is reduced to a semidefinite program which is an efficiently solvable optimization problem. Numerical examples are provided to illustrate the effectiveness of the proposed method.
In this paper, we develop a numerically efficient scheme for set-membership prediction and filtering for discrete-time nonlinear systems, that takes into explicit account the effects of nonlinearities via local second...
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In this paper, we develop a numerically efficient scheme for set-membership prediction and filtering for discrete-time nonlinear systems, that takes into explicit account the effects of nonlinearities via local second-order information. The filtering scheme is based on a classical prediction/update recursion that requires at each step the solution of a convex semidefinite optimization problem. The technical results discussed in the paper build upon the recently developed paradigm of uncertain linear equations (ULE) and semidefinite relaxations.
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