This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the st...
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This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the state and control are allowed to be indinifite here. When the generator matrix of the jump process - which is assumed to be a Markov chain - is known and time-invariant, the well-posedness of the indefinite stochastic LQ problem is shown to be equivalent to the solvability of a system of coupled generalized algebraic Riccati equations (CGAREs) that involves equality and inequality constraints. To analyze the CGAREs, linear matrix inequalities (LMIs) are utilized, and the equivalence between the feasibility of the LMIs and the solvability of the CGAREs is established. Finally, an LMI-based algorithm is devised to slove the CGAREs via a semidefinite programming, and numerical results are presented to illustrate the proposed algorithm.
A new method of enforcing the bounded realness of S parameter macro-model is proposed in this paper. With a given stable rational function obtained from fitting the original data, its closest bounded real rational fun...
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ISBN:
(纸本)0780381289
A new method of enforcing the bounded realness of S parameter macro-model is proposed in this paper. With a given stable rational function obtained from fitting the original data, its closest bounded real rational function is solved through semidefinite programming. This optimization problem is formulated through trace parameterization and uses minimal number of variables.
Variance control is one of the main themes in the stochastic control theory. The optimal LQ control with generalized covariance constraints (LQGCC) for the continuous linear time-invariant systems is studied in this p...
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ISBN:
(纸本)0780378962
Variance control is one of the main themes in the stochastic control theory. The optimal LQ control with generalized covariance constraints (LQGCC) for the continuous linear time-invariant systems is studied in this paper. This problem consists of two aspects: (1) the feasibility of the generalized covariance constrained control problem, which is to make the covariances of different controlled variables satisfy certain pre-specified covariance constraints;(2) the optimization of LQ performance over the feasible controller set. It is shown that the feasibility of the GCC problem is equivalent to the feasibility of several linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the controller set can be parameterized by the solutions of the LMIs. If the GCC is feasible, then the minimization of the LQ performance is equivalent to solving a semi-definite programming problem and our approach ensures the global optimality.
Using techniques developed in [1], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinit...
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ISBN:
(纸本)0780379241
Using techniques developed in [1], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite representation and a set of successively finer relaxations for the minimum rank problem on positive semidefinite matrices and for the minimum cardinality problem subject to linear inequalities.
Using outward rotations, we obtain an approximation algorithm for MAXn/2-UNCUT problem, i.e., partitioning the vertices of a weighted graph into two blocks of equalcardinality such that the total weight of edges that ...
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Using outward rotations, we obtain an approximation algorithm for MAXn/2-UNCUT problem, i.e., partitioning the vertices of a weighted graph into two blocks of equalcardinality such that the total weight of edges that do not cross the cut is maximized. In manyinteresting cases, the algorithm performs better than the algorithms of Ye and of Halperin andZwick. The main tool used to obtain this result is semidefinite programming.
Using techniques developed in [1], we show that some . minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefin...
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Using techniques developed in [1], we show that some . minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite representation and a set of successively finer relaxations for the minimum rank problem on positive semidefinite matrices and for the minimum cardinality problem subject to linear inequalities.
In order to gain insight into the quality of semidefinite relaxations of constrained quadratic 0/1 programming problems we study the quadratic knapsack problem. We investigate several basic semidefinite relaxations of...
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In order to gain insight into the quality of semidefinite relaxations of constrained quadratic 0/1 programming problems we study the quadratic knapsack problem. We investigate several basic semidefinite relaxations of this problem and compare their strength in theory and in practice. Various possibilities to improve these basic relaxations by cutting planes are discussed. The cutting planes either arise from quadratic representations of linear inequalities or from linear inequalities in the quadratic model. In particular, a large family of combinatorial cuts is introduced for the linear formulation of the knapsack problem in quadratic space. Computational results on a small class of practical problems illustrate the quality of these relaxations and cutting planes.
Free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary. ...
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Free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary. The case of one single load has been discussed in several recent papers, and an efficient numerical approach was presented in [M. Kocvara, M. Zibulevsky, and J. Zowe, RAIRO Model. Math. Anal. Numer., 32 (1998), pp. 255-281]. We attack here the multiload situation (understood in the worst-case sense), which is of much more interest for applications but also significantly more challenging from both the theoretical and the numerical points of view. After a series of transformation steps we reach a problem formulation for which we can prove existence of a solution;a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior point type are available. A number of numerical examples demonstrate the efficiency of our approach.
In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the nu-space framework, which is purely based on the symmetric primal-dual transformation and does not make...
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In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the nu-space framework, which is purely based on the symmetric primal-dual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weighted centers. Relations with other primal-dual maps are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.
We present a generalization of the Penalty/Barrier Multiplier algorithm for semidefinite programming, based on a matrix form of Lagrange multipliers. Our approach allows to use among others logarithmic, shifted logari...
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We present a generalization of the Penalty/Barrier Multiplier algorithm for semidefinite programming, based on a matrix form of Lagrange multipliers. Our approach allows to use among others logarithmic, shifted logarithmic, exponential and a very effective quadratic-logarithmic penalty/barrier functions. We present a dual analysis of the method, based on its correspondence to a proximal point algorithm with a nonquadratic distance-like function. We give computationally tractable dual bounds, which are produced by the Legendre transformation of the penalty function. Numerical results for large-scale problems from robust control, robust truss topology design and free material design demonstrate high efficiency of the algorithm.
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