Algorithms for unconstrained global optimization of nonlinear (polynomial) programming problems: The single and multi-segment polynomial B-spline approach

2017 ◽  
Vol 87 ◽  
pp. 205-220 ◽  
Author(s):  
D.D. Gawali ◽  
Ahmed Zidna ◽  
P.S.V. Nataraj
Keyword(s):  
Global Optimization ◽  
B Spline ◽  
Polynomial Programming

Electronic Cam Trajectory Generation Algorithm Based on Global Optimal Control Points of Non-Uniform B-Spline

2013 ◽  
Vol 418 ◽  
pp. 219-224 ◽  
Author(s):  
Shen Hang Wang ◽  
Jian Hua Hu ◽  
Yun Kuan Wang ◽  
Zheng Jun ◽  
Xiao Fei Qin ◽  
...  
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Control Point ◽  
Trajectory Generation ◽  
Control Points ◽  
Kinematic Constraints ◽  
Generation Algorithm ◽  
B Spline ◽  
Global Optimal ◽  
Trajectory Generation Algorithm

In order to improve the smoothness of electronic cam motion,an electronic cam trajectory generation algorithm based on global optimal control points of quintic non-uniform B-spline is prop-osed. This algorithm solves the problem of non-global optimization in existing approaches caused by transferring kinematic constraints into control point constraints to avoid the semi-infinite constraints problem. The interval ranges of the reserved free control point variables are calculated first, followed by partitioning and checking the subinterval with the property of the objective function and kinemat-ical constraints repeatedly until finding the global optimal control point. Compared with the existing control point constraints algorithm, the object function is optimized further and the electronic cam trajectory is smoother. Finally an practical example of electronic cam proves the effectiveness of the proposed algorithm.

scholarly journals Constrained global optimization of multivariate polynomials using polynomial B-spline form and B-spline consistency prune approach

2021 ◽  
Author(s):  
Deepak Devidasrao Gawali ◽  
Bhagyesh V. Patil ◽  
Ahmed Zidna ◽  
P. S. V. Nataraj
Keyword(s):  
Global Optimization ◽  
Global Minimum ◽  
Performance Metrics ◽  
Test Problems ◽  
Constrained Global Optimization ◽  
Multivariate Polynomial ◽  
Basic Algorithm ◽  
B Spline ◽  
Optimal Value ◽  
Improved Algorithm

In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. In improved algorithm we introduce several new ingredients, such as B-spline box consistency and B-spline hull consistency algorithm to prune the search regions and make the search more efficient. The performance of the basic and improved algorithm is tested and compared on set of test problems. The results of the tests show the superiority of the improved algorithm over the basic algorithm in terms of the chosen performance metrics. We compare optimal value of global minimum obtained using the proposed algorithms with CENSO, GloptiPoly and several state-of-the-art NLP solvers, on set of $11$ test problems. The results of the tests show the superiority of the proposed algorithm and CENSO solver (open source solver for global optimization of B-spline constrained problem) in that it always captures the global minimum to the user-specified accuracy.

scholarly journals Multi-parametric disaggregation technique for global optimization of polynomial programming problems

2011 ◽  
Vol 55 (2) ◽  
pp. 227-251 ◽  
Author(s):  
João P. Teles ◽  
Pedro M. Castro ◽  
Henrique A. Matos
Keyword(s):  
Global Optimization ◽  
Polynomial Programming
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