Considering a multi-user interference network with an eavesdropper, this paper investigates the problem of power allocation to optimize the worst secrecy throughput among the network links. Three scenarios for the acc...
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ISBN:
(纸本)9781538639207
Considering a multi-user interference network with an eavesdropper, this paper investigates the problem of power allocation to optimize the worst secrecy throughput among the network links. Three scenarios for the access of channel state information are considered: perfect channel state information, partial channel state information with channels from the transmitters to the eavesdropper exponentially distributed, and imperfectly known channels between the transmitters and the users with exponentially distributed errors. The paper develops various path-following procedures of low complexity and rapid convergence for the optimal power allocation. Their effectiveness and viability are illustrated through numerical examples. The power allocation schemes are shown to achieve high secrecy throughput.
We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. De...
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We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. Detailed examples are provided to illustrate the theory.
Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P* complementarity problems. Different from most ex...
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Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P* complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the "regularized central path" which exists for any continuous P* problem. It turns out that the algorithm is globally convergent for any P* problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.
We prove the superlinear convergence of the primal-dual infeasible interior-point path-following algorithm proposed recently by Kojima, Shida, and Shindoh and by the present authors, under two conditions: (i) the semi...
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We prove the superlinear convergence of the primal-dual infeasible interior-point path-following algorithm proposed recently by Kojima, Shida, and Shindoh and by the present authors, under two conditions: (i) the semidefinite programming problem has a strictly complementary solution;(ii) the size of the central path neighborhood approaches zero. The nondegeneracy condition suggested by Kojima, Shida, and Shindoh is not used in our analysis. Our result implies that the modified algorithm of Kojima, Shida, and Shindoh, which enforces condition (ii) by using additional corrector steps, has superlinear convergence under the standard assumption of strict complementarity. Finally, we point out that condition (ii) can be made weaker and show the superlinear convergence under the strict complementarity assumption and a weaker condition than (ii).
In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barri...
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In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see Yu. E. Nesterov and M.J. Todd, Math. Oper. Res., 22 (1997), pp. 1-42). The class of problems under consideration includes linear programming, semidefinite programming, and convex quadratically constrained, quadratic programming problems. For such problems we introduce a new definition of affine-scaling and centering directions. We present efficiency estimates for several symmetric primal-dual methods that can loosely be classified as path-following methods. Because of the special properties of these cones and barriers, two of our algorithms can take steps that typically go a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.
This paper provides a theoretical foundation for efficient interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems...
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This paper provides a theoretical foundation for efficient interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems we devise long-step and symmetric primal-dual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.
An infinite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered, We generalize the interior-point techniques of Nesterov-Nemirovsky to this in...
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An infinite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered, We generalize the interior-point techniques of Nesterov-Nemirovsky to this infinite-dimensional situation. The complexity estimates obtained are similar to finite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic constraints. It is shown that for this problem the Newton step is basically reduced to the standard LQ problem.
In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straight...
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ISBN:
(数字)9781611971453
ISBN:
(纸本)9780898713824
In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work.
The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.
We describe several adaptive-step primal-dual interior point algorithms for linear programming. All have polynomial time complexity while some allow very long steps in favorable circumstances. We provide heuristic rea...
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We describe several adaptive-step primal-dual interior point algorithms for linear programming. All have polynomial time complexity while some allow very long steps in favorable circumstances. We provide heuristic reasoning for expecting that the algorithms will perform much better in practice than guaranteed by the worst-case estimates, based on an analysis using a nonrigorous probabilistic assumption.
In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far from the boundary o...
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In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far from the boundary of the feasible set. Several parameterizations of this curve are described in primal and primal-dual problems, and it is shown how different algorithms are obtained by following the curve using different parameterizations. Polynomial algorithms are obtained by following the curve approximately, and this concept becomes precise by using explicit rules for measuring the proximity of a point in relation to the central path.
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