Quantum mechanics

Algorithm

Scale (ratio)

Derivation of the conjugate gradient method

Engineering

Aerospace engineering

Computer security

Nonlinear conjugate gradient method

Convergence (economics)

Gradient descent

RADIUS

Gradient method

Economics

Set (abstract data type)

Computer science

Mathematical optimization

Computer network

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Line search

Descent (aeronautics)

Mathematics

Asynchronous communication

Broyden–Fletcher–Goldfarb–Shanno algorithm

Conjugate residual method

Programming language

Economic growth

Artificial neural network

Conjugate gradient method

Machine learning

Journal of Mathematics

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem