• Journal of Integrative Natural Science
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• v.3 no.4
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• pp.241-245
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• 2010

In this paper, we study how to use CAS to solve certain minmax problems. More specifically, we reduce some to the problems about the packing of certain convex sets in the plane, and use Recognize algorithm to obtain good hypotheses for results. This method can be widely used to solve same types of mathematical problems.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.105-126
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• 2007

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.1-23
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• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• East Asian mathematical journal
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• v.4
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• pp.193-201
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• 1988

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.5
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• pp.361-367
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• 2014

In this paper, task scheduling and load balancing methods of multifrontal solution methods of finite element structural analysis in a modern multicore machine are introduced. Many structural analysis problems have generally irregular grid and many kinds of properties and materials. These irregularities and heterogeneities lead to bottleneck of parallelization and cause idle time to analysis. Therefore, task scheduling and load balancing are desired to reduce inefficiency. Several kinds of multithreaded parallelization methods are presented and comparison between static and dynamic task scheduling are shown. To reduce the idle time caused by irregular partitioned subdomains, computational load balancing methods, Balancing all tasks and minmax task pairing balancing, are invented. Theoretical and actual elapsed time are shown and the reason of their performance gap are discussed.