Quasi-Newton Methods: A New Direction

New hybrid conjugate gradient method for unconstrained optimization

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. Most of conjugate gradient methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analyses and implementations. Dai and Yuan (1999) proposed the conjugate gradient method which generates a descent direction at every iteration. Yabe and...

Planar Quasi - Newton Algorithms for Unconstrained Saddlepoint Problems

A new class of quasi-Newton methods is introduced that can locate a unique stationary point of an n-dimensional quadratic function in at most n steps. When applied to positive-definite or negative-definite quadratic functions, the new class is identical to Huang's symmetric family of quasi-Newton methods (Ref. 1). Unlike the latter, however, the new family can handle indefinite quadratic forms ...

Convergence of Finite -Dimensional Conjugate Direction and Quasi-Newton Methods for Singular Problems

A combined conjugate-gradient quasi-Newton minimization algorithm

Although quasi-Newton algorithms generally converge in fewer iterations than conjugate gradient algorithms, they have the disadvantage of requiring substantially more storage. An algorithm will be described which uses an intermediate (and variable) amount of storage and which demonstrates convergence which is also intermediate, that is, generally better than that observed for conjugate gradient...

Extra multistep BFGS updates in quasi-Newton methods

This note focuses on developing quasi-Newton methods that combine m+ 1 multistep and single-step updates on a single iteration for the sake of constructing the new approximation to the Hessian matrix to be used on the next iteration in computing the search direction. The approach considered here exploits the merits of the multistepmethods and those of El-Baali (1999) to create a hybrid techniqu...