A reinsurance problem is presented as a convex programming problem in Hilbert setup. The explicit form of the solution as well as the optimal reinsurance strategy is obtained.
A reinsurance problem is presented as a convex programming problem in Hilbert setup. The explicit form of the solution as well as the optimal reinsurance strategy is obtained.
We describe an infeasible interior point algorithm for convex minimization problems. The method uses quasi-Newton techniques for approximating the second derivatives and providing superlinear convergence. We propose a...
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We describe an infeasible interior point algorithm for convex minimization problems. The method uses quasi-Newton techniques for approximating the second derivatives and providing superlinear convergence. We propose a new feasibility control of the iterates by introducing shift variables and by penalizing them in the barrier problem. We prove global convergence under standard conditions on the problem data, without any assumption on the behavior of the algorithm.
作者：
Wu, CWIBM Corp
Div Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA
There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analyt...
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There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analytical criteria for global or local synchronization. The second class of results relies on linearization around the synchronization manifold and the computation of Lyapunov exponents. The computation of Lyapunov exponents is mainly done via numerical experiments and can only show local synchronization in the neighborhood of the synchronization manifold. On the other hand, Lyapunov's direct method is more rigorous and can give global results. The coupling topology is generally expressed in matrix form and the first class of methods mainly deals with symmetric matrices whereas the second class of methods can work with all diagonalizable matrices. The purpose of this brief is to bridge the gap in the applicability of the two classes of methods by considering the nonsymmetric case-for the first class of methods. We derive a synchronization criterion for nonreciprocal coupling related to a numerical quantity that depends on the coupling topology and we present methods for computing this quantity.
作者：
L.M.Gra■a DrummondA.N.IusemB.F.SvaiterPrograma de Engenharia de Sistemas de Computacao
COPPE-UFRJCP 68511Rio de Janeiro-RJ21945970BrazilInstituto de Matematica Pura e Aplicada (IMPA) Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320BrazilInstituto de Matematica Pura e Aplicada (IMPA)Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320Brazil
We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presentin...
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We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presenting some well known existence results for these problems, based on a scalarization approach, we establish necessity of the optimality conditions under a Slater-like constraint qualification, and then sufficiency for the K-convex case. We present two alternative sets of optimality conditions, with the same properties in connection with necessity and sufficiency, but which are different with respect to the dimension of the spaces to which the dual multipliers belong. We introduce a duality scheme, with a point-to-set dual objective, for which strong duality holds. Some examples and open problems for future research are also presented.
In the last two decades, the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization. These advances have recently started to significantly impact v...
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In the last two decades, the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization. These advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential. This paper focuses on two such fields: digital signal processing and communication. In the past, the widely used optimization methods in both fields had been the gradient descent or least squares methods, both of which are known to suffer from the usual headaches of stepsize selection, algorithm initialization and local minima. With the recent advances in conic and robust optimization, the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication. This paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields. The successful applications considered in this paper include adaptive filtering, robust beamforming, design and analysis of multi-user communication system, channel equalization, decoding and detection. Throughout, our emphasis is on how to exploit the hidden convexity, convex reformulation of semi-infinite constraints, analysis of convergence, complexity and performance, as well as efficient practical implementation.
In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the non...
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In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem.
A general decomposition framework for solving large-scale convex programming problems is described. New algorithms are obtained and several known techniques are recovered as special cases, including Dantzig-Wolfe colu...
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A general decomposition framework for solving large-scale convex programming problems is described. New algorithms are obtained and several known techniques are recovered as special cases, including Dantzig-Wolfe column generation, the finite envelope method of Rockafellar, and Zhu's primal-dual steepest descent method.
A cutting plane method for linear programming is described. This method is an extension of Atkinson and Vaidya's algorithm, and uses the central trajectory. The logarithmic barrier function is used explicitly, mot...
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A cutting plane method for linear programming is described. This method is an extension of Atkinson and Vaidya's algorithm, and uses the central trajectory. The logarithmic barrier function is used explicitly, motivated partly by the successful implementation of such algorithms. This makes it possible to maintain primal and dual iterates, thus allowing termination at will, instead of having to solve to completion. This algorithm has the same complexity (O(nL(2)) iterations) as Atkinson and Vaidya's algorithm, but improves upon it in that it is a "long-step" version, while theirs is a "short-step" one in some sense. For this reason, this algorithm is computationally much more promising as well. This algorithm can be of use in solving combinatorial optimization problems with large numbers of constraints, such as the Traveling Salesman Problem.
A primal-dual active set method for quadratic problems with bound constraints is presented. Based on a guess on the active set, a primal-dual pair (x, s) is computed that satisfies the first order optimality condition...
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A primal-dual active set method for quadratic problems with bound constraints is presented. Based on a guess on the active set, a primal-dual pair (x, s) is computed that satisfies the first order optimality condition and the complementarity condition. If (x, s) is not feasible, a new active set is determined, and the process is iterated. Sufficient conditions for the iterations to stop in a finite number of steps with an optimal solution are provided. Computational experience indicates that this approach often requires only a few (less than 10) iterations to find the optimal solution.
In this paper we address the issue of improving transmission security in a deregulated power market. We propose an optimization procedure that assures that transmission security is maintained, and generates minimal co...
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ISBN:
(纸本)0780366387
In this paper we address the issue of improving transmission security in a deregulated power market. We propose an optimization procedure that assures that transmission security is maintained, and generates minimal corrections in existing contractual transactions that are necessary to ensure security. Our procedure is based on a DC load flow, and as such it is intended as a screening tool, and a source of candidate control actions that will be later refined by a more accurate (AC) model. Our approach may also enable faster calculations of important operational quantities like Available Transfer Capability (ATC).
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