Discrete mathematics

Mathematics

Line search

Algorithm

Mathematical optimization

Gradient method

Gradient descent

Topological conjugacy

Mathematical analysis

RADIUS

Artificial intelligence

Conjugate

Derivation of the conjugate gradient method

Nonlinear conjugate gradient method

Computer science

Computation

Conjugacy class

Conjugate residual method

Computer security

Artificial neural network

Conjugate gradient method

Biconjugate gradient method

The paper presents some open problems associated to the nonlin- ear conjugate gradient algorithms for unconstrained optimization. Mainly, these problems refer to the initial direction, the conjugacy condition, the step length computation, new formula for conjugate gradient parameter computation based on function's values, the inuence of accuracy of line search procedure, how we can take the problem's structure on conjugate gradient algorithms, how we can consider the second order information in these algorithms, what the most conve- nient restart procedure is, what the best hybrid conjugate gradient algorithm is, scaled conjugate gradient algorithms, what the most suitable stopping criterion in conjugate gradient algorithms is, etc.

Open Problems in Nonlinear Conjugate Gradient Algorithms for Unconstrained Optimization