Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...

A line search method is proposed for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function. Global convergence properties of this method was analyzed in a companion paper. Here a simple modification of the method introducing second order correction steps is presented. It is shown that the proposed method does not suffer from the Maratos ...

Minimization of unconstrained objective function in the form of mathematical expectation is considered. Sample Average Approximation SAA method transforms the expectation objective function into a real-valued deterministic function using large sample and thus deals with deterministic function minimization. The main drawback of this approach is its cost. A large sample of the random variable tha...

and Applied Analysis 3 = ‖d k−1 ‖2 ‖g k−1 ‖4 + 1 ‖g k ‖2 − β2 k (gT k d k−1 ) 2 /‖g k ‖4

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semideenite is exhibited for this class of algorithms ...

Due to the variety of products, simultaneous production of different models has an important role in production systems. Moreover, considering the realistic constraints in designing production lines attracted a lot of attentions in recent researches. Since the assembly line balancing problem is NP-hard, efficient methods are needed to solve this kind of problems. In this study, a new hybrid met...

Discrete-event simulation based optimization is the process of finding the optimum design of a stochastic system when the performance measure(s) could only be estimated via simulation. Randomness in simulation outputs often challenges the correct selection of the optimum. We propose an algorithm that merges Ranking and Selection procedures with a large class of random search methods for continu...