scholarly journals Optimally rotated vectors

2003 ◽  
Vol 2003 (63) ◽  
pp. 4015-4023 ◽  
Author(s):  
Morteza Seddighin
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
Systems Of Nonlinear Equations ◽  
Real Numbers ◽  
Lagrange Multiplier Technique ◽  
The Matrix

We study vectors which undergo maximum or minimum rotation by a matrix on the field of real numbers. The cosine of the angle between a maximally rotated vector and its image under the matrix is called the cosine or antieigenvalue of the matrix and has important applications in numerical methods. Using Lagrange multiplier technique, we obtain systems of nonlinear equations which represent these optimization problems. Furthermore, we solve these systems symbolically and numerically.

scholarly journals Cooperative Multi-Simplex Algorithm: An Innovation from Localization to Globalization

2020 ◽  
Author(s):  
Javaid Ali
Keyword(s):  
Comparative Analysis ◽  
Local Search ◽  
Nonlinear Equations ◽  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Simplex Algorithm ◽  
Systems Of Nonlinear Equations ◽  
Vertex Sharing ◽  
Sharing Strategy ◽  
Analysis Of Results

This study suggests a novel cooperative multi-simplex algorithm that generalizes a local search optimizer to design a novel global search heuristic algorithm. The proposed algorithm exploits the vertex sharing strategy to enhance the search abilities of the working simplexes. The vertex sharing among the simplexes is carried out through cooperative step that is based on fitness of the underlying simplex. The proposed algorithm is applied to solve some systems of nonlinear equations by transforming them to optimization problems. Comparative analysis of results shows that the proposed method is practical and effective.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations
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