Alternative Algorithms of Broyden Familyami: For Unconstrained Optimization

New Conjugate Gradient Method Addressing Large Scale Unconstrained Optimization Problem

“… with impressive performance is introduced in order to achieve optimal solutions. For the next interest, this new coefficient can be extended in hybrid between CG and BFGS methods with the search direction proposed by [8]- [11].…”

The algorithms of Broyden-CG for unconstrained optimization problems

“…Hence, the modification of the quasi-Newton method by previous researchers spawned the new idea of hybridizing the classical method to yield the new hybrid method such as in [10][11][12][13]. Hence, this study proposes a new hybrid search direction that combines the concept of search direction of the quasi-Newton and CG methods.…”

An improved BFGS search direction using exact line search for solving unconstrained optimization problems

“…Hybrid search direction in Quasi-Newton for BFGS update Hessian is the newborn in the optimization area and it was proposed by [13][14][15] using the Quasi-Newton search direction and standard steepest descent gradient then continued by [22] using the same technique with exact line search procedures and they were proven to be super linear and globally converge with Wolfe conditions (1.8) and (1.9) is satisfied. Then, the research using hybrid search direction on Quasi-Newton for solving unconstrained optimization problems was continued by [9] using the inexact line search in Broyden family update Hessian and they were proven to converge efficiently for the unconstrained optimization problems tested. However, all the hybrid search direction in [13][14][15], [22] and [9] do not have the parameter boundary and this stuation will lead to the possibility of failure to the method for solving some of the unconstrained optimization.…”

“…Then, the research using hybrid search direction on Quasi-Newton for solving unconstrained optimization problems was continued by [9] using the inexact line search in Broyden family update Hessian and they were proven to converge efficiently for the unconstrained optimization problems tested. However, all the hybrid search direction in [13][14][15], [22] and [9] do not have the parameter boundary and this stuation will lead to the possibility of failure to the method for solving some of the unconstrained optimization. Hence, proposed in this paper is the new hybrid search direction using the conjugate gradient idea this method can be consider one of continuum of the method that written in [18].…”

“…For all the line search procedures, it was divided into two types that are using the exact line search and another one is without exact line search as proposed by [4], [19], [20] and others. However, this paper only considered BFGS algorithm using the exact line search as suggested by [7], [22], [12] and [9] that is…”