Steffen's Flexible Polyhedron

2007 ◽  
Keyword(s):  
Flexible Polyhedron

A Weighted Flexible Tolerance Algorithm for Constrained Minimization

1975 ◽  
Vol 97 (4) ◽  
pp. 1291-1294 ◽  
Author(s):  
M. A. Townsend ◽  
F. Y. Lam
Keyword(s):  
Objective Function ◽  
Search Algorithm ◽  
Inequality Constraints ◽  
Constrained Minimization ◽  
Rapid Convergence ◽  
Flexible Polyhedron ◽  
Equality And Inequality Constraints ◽  
Direct Search Algorithm ◽  
Tolerance Method ◽  
Nonlinear Equality

A direct search algorithm based upon the flexible tolerance method developed by Paviani and Himmelblau [1] for minimization of a functional subject to nonlinear equality and inequality constraints is proposed and evaluated. The modification incorporates a weighting on the direction of search in which the flexible polyhedron formed orients itself toward the gradient of the objective function (and clings to all active constraints). This is accomplished by weighting the centroid, in the sense of minimization, of the polyhedron with respect to the objective function. A number of problems have been solved satisfactorily by this algorithm, generally with more rapid convergence.

On the problem of invariance of the volume of a flexible polyhedron

1995 ◽  
Vol 50 (2) ◽  
pp. 451-452 ◽  
Author(s):  
I Kh Sabitov
Keyword(s):  
Flexible Polyhedron

An analog of the flexible polyhedron method for scheduling problems

1988 ◽  
Vol 41 (4) ◽  
pp. 1106-1110
Author(s):  
Yu. D. Elizarov ◽  
E. L. Stolov
Keyword(s):  
Scheduling Problems ◽  
Flexible Polyhedron ◽  
Polyhedron Method

Gas Lubrication of a Ringless Piston in an Internal Combustion Engine Under Dynamic Loading

1988 ◽  
Vol 110 (4) ◽  
pp. 718-726 ◽  
Author(s):  
Z. P. Mourelatos
Keyword(s):  
Theoretical Model ◽  
Dynamic Loading ◽  
Internal Combustion Engines ◽  
Combustion Engine ◽  
Correction Term ◽  
Internal Combustion ◽  
Minimization Method ◽  
Flexible Polyhedron ◽  
Side Load ◽  
Gas Lubrication

A theoretical model is presented to solve the transient, two-dimensional, compressible Reynolds equation for a gas bearing. The Newton-Raphson method is used on the governing nonlinear Reynolds equaion while the Galerkin’s method is employed to solve the resulting linear equations for the correction term. The numerical solution of the pressure distribution of an infinitely long, plane-wedge, slider bearing compares very well with the analytical (exact) solution. This theoretical model is then used to calculate the trajectory of a ringless piston within the cylinder of an I. C. engine under a given dynamic loading. The flexible polyhedron unconstrained minimization method is used to find the equilibrium position of the piston within the cylinder for each crankangle. It was found that a 40 mm long ringless piston can support a uniform side load of about 50 Newtons at 2000 r/min running on a gas film. However, the same piston can sustain a nonuniform side load with a much higher peak value (three to five times the uniform load) which lasts approximately 20 to 30 degrees of crankangle only. The sustainable side load by gas lubrication is much lower than the peak piston side load of conventional internal combustion engines.

A Parameter Selection Method for Support Vector Interval Regression Model

2011 ◽  
Vol 66-68 ◽  
pp. 626-630
Author(s):  
Yong Qi Chen
Keyword(s):  
Regression Model ◽  
Optimization Algorithm ◽  
Search Algorithm ◽  
Selection Method ◽  
Support Vector ◽  
Regression Result ◽  
Imprecise Data ◽  
Flexible Polyhedron ◽  
Model Experiments ◽  
Parameters Selection

The support vector interval regression model is an effective method to estimate imprecise data. Parameters of this model is very important in order to obtain the excellent regression result. The flexible polyhedron search algorithm is a fast optimization algorithm. Based on the flexible polyhedron search algorithm, this paper proposes an automatic parameters selection method for the support vector interval regression model. Experiments illustrate the validity and applicability of the support vector interval regression model based on the flexible polyhedron search algorithm.

Optimal fuzzy PID controller with adjustable factors based on flexible polyhedron search algorithm

2002 ◽  
Vol 9 (2) ◽  
pp. 128-133 ◽  
Author(s):  
Guan-zheng Tan ◽  
Hong-feng Xiao ◽  
Yue-chao Wang
Keyword(s):  
Pid Controller ◽  
Search Algorithm ◽  
Fuzzy Pid ◽  
Flexible Polyhedron ◽  
Fuzzy Pid Controller
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