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991.
This paper proposes a multi-stage decision procedure to cope with a hierarchical multiple objective decision environment in which the upper-level DM only provides partial preference information and the lower-level DM is fuzzy about the tradeoff questions such that to achieve substantially more than or equal to some values is delivered to maximize the objectives. Therefore, the procedure consists of two levels, a upper-level and a lower-level. The main idea is that after the upper-level provides partial preference information to the lower-level as a guideline of decision, the lower-level DM determines a satisfactory solution from the reduced non-dominated set in the framework of multi-objective fuzzy programs. 相似文献
992.
Tim Van Voorhis 《Journal of Global Optimization》2002,24(3):349-370
Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure. 相似文献
993.
Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method. 相似文献
994.
In several applications, underestimation of functions has proven to be a helpful tool for global optimization. In protein–ligand
docking problems as well as in protein structure prediction, single convex quadratic underestimators have been used to approximate
the location of the global minimum point. While this approach has been successful for basin-shaped functions, it is not suitable
for energy functions with more than one distinct local minimum with a large magnitude. Such functions may contain several
basin-shaped components and, thus, cannot be underfitted by a single convex underestimator. In this paper, we propose using
an underestimator composed of several negative Gaussian functions. Such an underestimator can be computed by solving a nonlinear
programming problem, which minimizes the error between the data points and the underestimator in the L
1 norm. Numerical results for simulated and actual docking energy functions are presented. 相似文献
995.
B. Aghezzaf 《Journal of Mathematical Analysis and Applications》2003,285(1):97-106
Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order (F,ρ)-convexity assumptions. These results generalize the duality results recently given by Aghezzaf and Hachimi involving generalized first order (F,ρ)-convexity conditions. 相似文献
996.
In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on
nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented.
Dedicated to Prof. Mariano Gasca on the occasion of his 60th birthday. 相似文献
997.
We study four measures of problem instance behavior that might account for the observed differences in interior-point method
(IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry
measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-)
condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the
level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure
the sample correlation (CORR) between these measures and IPM iteration counts (solved using the software SDPT3) when these
measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with
IPM iterations (CORR = 0.901), and provides a very good explanation of IPM iterations, particularly for problem instances
with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence
of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal
solution is essentially uncorrelated with IPM iterations.
This research has been partially supported through the MIT-Singapore Alliance. 相似文献
998.
G. Alkauskas 《Lithuanian Mathematical Journal》2003,43(2):103-110
In this article, we give a new proof of the Rödseth–Gupta theorem on binary partitions and give one possible generalization of this theorem. 相似文献
999.
Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve NLP problems of typical sizes. However stochastic programming problems are highly structured. The key to the efficient solution of such problems is therefore the ability to exploit their structure. Interior point methods are well-suited to the solution of very large non-linear optimization problems. In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semi-variance, skewness or non-linear utility functions in the objective, can be solved with the state-of-the-art solver. 相似文献
1000.
In this article we introduce the difference sequence space m(M, Δ, φ) using the Orlicz function. We study its different properties like solidity, completeness etc. Also we obtain some inclusion
relations involving the space m(M, Δ, φ).
相似文献