scholarly journals Piecewise-Linear Pathways to the Optimal Solution Set in Linear Programming

1997 ◽  
Vol 93 (3) ◽  
pp. 619-634 ◽  
Author(s):  
M. Ç. Pinar
Keyword(s):  
Linear Programming ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Solution Set ◽  
Optimal Solution Set

CFD Based Multi-Disciplinary Optimization Design of High-Performance Deep Sea Seismic Vessel

2017 ◽  
Author(s):  
Mao Xiaofei ◽  
Zhang Wenxu ◽  
Qian Jiankui ◽  
Wu Minghao
Keyword(s):  
High Performance ◽  
Optimization Design ◽  
Optimal Solution ◽  
Solution Set ◽  
Short Term ◽  
Hull Form ◽  
Optimal Solution Set ◽  
Computational Fluid Dynamics Cfd ◽  
The Stability

This paper focuses on the application of a ship hull form multi-disciplinary optimization (MDO) system based on the computational fluid dynamics (CFD). Using the iSIGHT software, the MDO system integrates an automatic geometry transformation program and high-fidelity CFD solvers for different sub-disciplines. Hydrodynamics analysis subsystem includes resistance, seakeeping and stability modules. The resistance and seakeeping is analyzed by commercial potential-flow CFD codes, the stability is assessed by in-house code. The geometry variation output can be automatically used by the numerical solvers. By means of the design of experiment (DOE) technique, a neural network metamodel is trained to predict short term motion response of the derived ships efficiently. The system has been used in a seismic vessel’s hull form optimization to minimize the resistance and maximize the long term seakeeping operability index. Meanwhile, the stability in waves is concerned as a constraint. The hybrid MIGA-NLPQL optimization algorithm is applied for a global-to-local search in resistance optimization. For the synthesis optimization, a Pareto optimal solution set has been obtained and the final solution is achieved by trade-off analysis of the solution set. The entire automatic optimization process can be used for the preliminary design of new high performance vessels.

scholarly journals Training v-Support Vector Classifiers: Theory and Algorithms

2001 ◽  
Vol 13 (9) ◽  
pp. 2119-2147 ◽  
Author(s):  
Chih-Chung Chang ◽  
Chih-Jen Lin
Keyword(s):  
Support Vector Machine ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Large Scale ◽  
Optimal Solution ◽  
Solution Set ◽  
Support Vector ◽  
Support Vectors ◽  
Optimal Solution Set

The ν-support vector machine (ν-SVM) for classification proposed by Schölkopf, Smola, Williamson, and Bartlett (2000) has the advantage of using a parameter ν on controlling the number of support vectors. In this article, we investigate the relation between ν-SVM and C-SVM in detail. We show that in general they are two different problems with the same optimal solution set. Hence, we may expect that many numerical aspects of solving them are similar. However, compared to regular C-SVM, the formulation of ν-SVM is more complicated, so up to now there have been no effective methods for solving large-scale ν-SVM. We propose a decomposition method for ν-SVM that is competitive with existing methods for C-SVM. We also discuss the behavior of ν-SVM by some numerical experiments.

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