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71.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
72.
J. T. Haslinger K. Kunisch G. Peichl 《Computational Optimization and Applications》2003,26(3):231-251
This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers. 相似文献
73.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献
74.
This paper develops a theory for the global solution of nonconvex optimization problems with parameter-embedded linear dynamic systems. A quite general problem formulation is introduced and a solution is shown to exists. A convexity theory for integrals is then developed to construct convex relaxations for utilization in a branch-and-bound framework to calculate a global minimum. Interval analysis is employed to generate bounds on the state variables implied by the bounds on the embedded parameters. These bounds, along with basic integration theory, are used to prove convergence of the branch-and-bound algorithm to the global minimum of the optimization problem. The implementation of the algorithm is then considered and several numerical case studies are examined thoroughly 相似文献
75.
This paper presents a new generic Evolutionary Algorithm (EA) for retarding the unwanted effects of premature convergence. This is accomplished by a combination of interacting generic methods. These generalizations of a Genetic Algorithm (GA) are inspired by population genetics and take advantage of the interactions between genetic drift and migration. In this regard a new selection scheme is introduced, which is designed to directedly control genetic drift within the population by advantageous self-adaptive selection pressure steering. Additionally this new selection model enables a quite intuitive heuristics to detect premature convergence. Based upon this newly postulated basic principle the new selection mechanism is combined with the already proposed Segregative Genetic Algorithm (SEGA), an advanced Genetic Algorithm (GA) that introduces parallelism mainly to improve global solution quality. As a whole, a new generic evolutionary algorithm (SASEGASA) is introduced. The performance of the algorithm is evaluated on a set of characteristic benchmark problems. Computational results show that the new method is capable of producing highest quality solutions without any problem-specific additions. 相似文献
76.
Whilst the space volume of muffler in noise control system is often constrained for maintenance in practical engineering work, the maximization on muffler’s performance becomes important and essential. In this paper, a novel approach genetic algorithms (GAs) based on the principles of natural biological evolution will be used to tackle this optimization of muffler design [M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, MA, 1996]. Here, the shape optimization of multi-segments muffler coupled with the GA searching technique is presented. The techniques of binary genetic algorithms (BGA) together with the commercial MATLAB package [G. Lindfield, J. Penny, Numerical Method Using Matlab, second ed., Prentice Hall, Englewood Cliffs, NJ, 2000] are applied in GA searching. In addition, a numerical case of pure tone elimination with 2-5 segments on muffler is introduced and fully discussed. To achieve the best optimization in GA, several GA parameters are on trial in various values. Results show that the GA operators, including crossover mutation and elitism, are essential in accuracy. Consequently, results verify that the optimal sound transmission loss at the designed frequency of 500 Hz is exactly maximized. The GA optimization on multi-segments muffler proposed in this study surely provides a quick and correct approach. 相似文献
77.
L.G. Casado I. García T. Csendes V.G. Ruíz 《Journal of Optimization Theory and Applications》2003,118(1):27-43
Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach. 相似文献
78.
79.
Arnold Neumaier 《Journal of Global Optimization》2003,25(2):175-181
A family of multivariate rational functions is constructed. It has strong local minimizers with prescribed function values at prescribed positions. While there might be additional local minima, such minima cannot be global. A second family of multivariate rational functions is given, having prescribed global minimizers and prescribed interpolating data. 相似文献
80.
构造一个求解椭圆型边值问题的多子域D—N交替算法,导出对应的容度方程和等价的迭代法,证明算法的收敛性。 相似文献