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91.
Monique Laurent 《Mathematical Programming》2007,109(2-3):239-261
We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras.
The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located
between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with
O(n
7) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n
3), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s
bound with the same computational complexity.
Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203. 相似文献
92.
The article concerns heterojunction resonant cavity-enhanced (RCE) Schottky photodiodes with GaAs in the absorption layer. The quantum efficiency and linear pulse response have thoroughly been analysed. For the first time, the response of a heterojunction photodiode has been modelled by the phenomenological model for a two-valley semiconductor. The results obtained have shown that the satellite valleys, as well as the parasitic time constant, significantly influence the response and, accordingly, have to be taken into account when analysing and optimizing RCE photodetectors. 相似文献
93.
René Meziat Diego Patiño Pablo Pedregal 《Computational Optimization and Applications》2007,38(1):147-171
We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control
problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control
variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex
optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on
global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking
of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also
present the numerical schemes to solve several examples arising in science and technology. 相似文献
94.
A review of the optimal stopping problem with more than a single decision maker (DM) is presented in this paper. We classify
the existing literature according to the arrival of the offers, the utility of the DMs, the length of the sequence of offers,
the nature of the game and the number of offers to be selected. We enumerate various definitions for this problem and describe
some dynamic approaches.
Fouad Ben Abdelaziz is on leave from the Institut Superieur de Gestion, University of Tunis, Tunisia e-mail: foued.benabdelaz@isg.run.tn. 相似文献
95.
Discrete global descent method for discrete global optimization and nonlinear integer programming 总被引:2,自引:0,他引:2
A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization
problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function
f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function.
The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers
of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer
variables and up to 1.38 × 10104 feasible points have demonstrated the applicability and efficiency of the proposed method. 相似文献
96.
In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques. 相似文献
97.
In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd > 0 is a constant depending on the problem dimension and data. 相似文献
98.
A combined programming and iteration algorithm for finite element analysis of three-dimensional contact problems 总被引:3,自引:0,他引:3
Comparing with two-dimensional contact problems, three-dimensional frictional contact problems are more difficult to deal
with, because of the unknown slip direction of the tangential force and enormous computing time. In order to overcome these
difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is derived in this paper. The iteration
algorithm, which alleviates the difficulty of unknown slip direction, is used along with the PQP method to cut down computing
costs. Numerical example is given to demonstrate the validity of the present algorithm.
The project supported by the Machinary and Electronics Ministry of China 相似文献
99.
Dashan Huang Yoshitaka Kai Frank J. Fabozzi Masao Fukushima 《European Journal of Operational Research》2007
This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool’s cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC’s scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model. 相似文献
100.
C. Bogani M. G. Gasparo A. Papini 《Journal of Optimization Theory and Applications》2007,134(1):47-59
We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search
methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that
it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to
ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical
experiments seem to be encouraging.
This work was supported by M.U.R.S.T., Rome, Italy. 相似文献