Convergence analysis of a new conjugate gradient method for unconstrained optimization

Abstract

In this paper, the convergence analysis of a proposed new conjugate gradient method for unconstrained optimization problems was considered. This method inherits an important property of Polak-Ribiere-Polyak (PRP). Under the exact line search condition, we established the descent condition of the method as well as the global convergence of the method. Numerical results show that our formula is effective by comparing with some existing formulas.

A Weighted Analytic Center for Second-Order Cone Constraints

“…This section introduces weighted analytic center for the system of second order cone constraints (1).…”

“…Table 2 describes the 31 random test problems used for our numerical experiments. For each SOC test problem, integer values q and n are generated uniformly in the intervals [1,6] and [2,10] respectively. Then q m ∈ ℤ is generated such that each entry i m is uniform in the interval [1,10].…”

“…For each SOC test problem, integer values q and n are generated uniformly in the intervals [1,6] and [2,10] respectively. Then q m ∈ ℤ is generated such that each entry i m is uniform in the interval [1,10]. After this, q SOCs of the form 0…”

“…denotes the feasible region defined by the SOC constraints in (1). Assume R is bounded and that it has a non-empty interior.…”

“…CG methods are popular for solving large scale non-linear unconstrained optimization problems. They are characterized by strong global convergence properties and low memory requirement [1]. CG methods use only the gradient of the barrier function.…”