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991.
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative
2-graded algebras tending in a suitable limit to a dense subalgebra of the
2-graded algebra of
∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the “fuzzy level”. 相似文献
992.
The nonlinear rescaling principle (NRP) consists of transforming the objective function and/or the constraints of a given
constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal
set of solutions coincides. A nonlinear transformation parameterized by a positive scalar parameter and based on a smooth
sealing function is used to transform the constraints. The methods based on NRP consist of sequential unconstrained minimization
of the classical Lagrangian for the equivalent problem, followed by an explicit formula updating the Lagrange multipliers.
We first show that the NRP leads naturally to proximal methods with an entropy-like kernel, which is defined by the conjugate
of the scaling function, and establish that the two methods are dually equivalent for convex constrained minimization problems.
We then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy-like proximal
methods for convex constrained optimization problems. Special cases of the nonlinear rescaling algorithm are presented. In
particular a new class of exponential penalty-modified barrier functions methods is introduced.
Partially supported by the National Science Foundation, under Grants DMS-9201297, and DMS-9401871.
Partially supported by NASA Grant NAG3-1397 and NSF Grant DMS-9403218. 相似文献
993.
Quasi-Newton method by Hermite interpolation 总被引:1,自引:0,他引:1
T. F. Sturm 《Journal of Optimization Theory and Applications》1994,83(3):587-612
This paper describes a new attempt to solve the problem of computing a local minimizer of a sufficiently often differentiable unconstrained objective function. In every step of the iteration, a special Hermite interpolant is constructed. Old iteration points serve as points of support with the function value and gradient information. This yields a quasi-Newton algorithm with quadratic convergence order. 相似文献
994.
Analterable digraph is a digraph with a subset of its edges marked alterable and their orientations left undecided. We say that an alterable digraph has an invariant ofk on the length of the longest circuit if it has a circuit of length at leastk regardless of the orientations over its alterable edges. Computing the maximum invariant on the length of the longest circuit in an alterable digraph is aglobal optimization problem. We show that it is hard to approximate the global optimal solution for the maximum invariant problem.Research supported in part by NSF grant CCR 9121472. 相似文献
995.
Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods. 相似文献
996.
There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages. 相似文献
997.
998.
Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model. 相似文献
999.
Hoang Tuy 《Journal of Global Optimization》2007,37(2):321-323
A counter-example is given to several recently published results on duality bound methods for nonconvex global optimization. 相似文献
1000.
Bahram Alidaee Fred Glover Gary Kochenberger Haibo Wang 《European Journal of Operational Research》2007
The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach. 相似文献