Newton’s Method for Optimization Problems with Equality Constraints

1974 ◽  
Vol 11 (5) ◽  
pp. 874-886 ◽  
Author(s):  
R. A. Tapia
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Optimization Problems ◽  
Equality Constraints

On q-Newton’s method for unconstrained multiobjective optimization problems

2020 ◽  
Vol 63 (1-2) ◽  
pp. 391-410 ◽  
Author(s):  
Shashi Kant Mishra ◽  
Geetanjali Panda ◽  
Md Abu Talhamainuddin Ansary ◽  
Bhagwat Ram
Keyword(s):  
Multiobjective Optimization ◽  
Newton’S Method ◽  
Newton's Method ◽  
Optimization Problems ◽  
Multiobjective Optimization Problems

scholarly journals An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jibum Kim
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Mesh Optimization ◽  
Efficient Approach ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Objective Function ◽  
Surface Constraints ◽  
Derivatives Of

We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton’s method, which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality.

scholarly journals On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 616
Author(s):  
Kin Keung Lai ◽  
Shashi Kant Mishra ◽  
Bhagwat Ram
Keyword(s):  
Multiobjective Optimization ◽  
Newton’S Method ◽  
Newton's Method ◽  
Global Minimum ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Hessian Matrix ◽  
Step Length ◽  
Positive Definite ◽  
Multiobjective Optimization Problems

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

Sign in / Sign up

Export Citation Format

Share Document