Ismail Mohd

The proof of sufficient descent condition for a new type of conjugate gradient methods

Conjugate gradient methods are effective in solving linear equations and solving non-linear optimization. In this work we compare our new conjugate gradient coefficient βk with classical formula under strong Wolfe line search; our method contains sufficient descent condition. Numerical results have shown that the new βk performs better than classical formula.Conjugate gradient methods are effective in solving linear equations and solving non-linear optimization. In this work we compare our new conjugate gradient coefficient βk with classical formula under strong Wolfe line search; our method contains sufficient descent condition. Numerical results have shown that the new βk performs better than classical formula.

Interval elimination method for stochastic spanning tree problem

Abstract The optimum spanning tree problem has been well considered and until now several powerful algorithms have been proposed. This problem has been generalized toward a stochastic spanning tree problem in which edge weights are not constant but random variables. A method called an interval elimination is used for solving the stochastic spanning tree problem which has been transformed into its proxy deterministic equivalent problem.

Constraint exploration method for quadratic programming problem

In this paper, we represent a method which is based on the violated constraints by the unconstrained minimum of the objective function of the quadratic programming problem for exploring, locating and computing the optimal solution of the problem without using additional information as have been done in most of the favourite established methods.

A new conjugate gradient method for unconstrained optimization with sufficient descent

Conjugate gradient (CG) methods represent an important computational innovation in solving large-scaled unconstrained optimization problems. There are many different versions of CG methods. Although some methods are equivalent to each other, their performances are quite different. This paper presents a new CG method based on modification of the original CG methods. The important criteria of this new CG method are its global convergence properties. Numerical result shows that this new CG method performs better than the original CG methods.

Solving unconstrained optimization with a new type of conjugate gradient method

Conjugate gradient (CG) methods have been widely used as schemes to solve large-scale unconstrained optimization problems. Numerous studies and modifications have been done recently to improve this method. In this paper, we proposed a new type of CG coefficients (βk) by modification of Polak and Ribiere (PR) method. This new βk is shown to possess global convergence properties by using exact line searches. Performance comparisons are made with the four most common βk proposed by the early researches. Numerical results also show that this new βk performed better.

A new modification of Hestenes-Stiefel method with descent properties

Conjugate gradient (CG) methods are important for large-scale unconstrained optimization due to its low memory requirements and global convergence properties. Numerous researches has been done to proposed new CG coefficients and to improve the efficiency. In this paper, we proposed a new CG coefficient based on the original Hestenes-Steifel CG coefficient. The global convergence result is established using exact line search. Most of our numerical results show that our method is very efficient when compared to the early CG coefficients for a given standard test problems.

MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

A new steepest descent method

The classical steepest descent (SD) method is known as one of the earliest and the best method to minimize a function. Even though the convergence rate is quite slow, but its simplicity has made it one of the easiest methods to be used and applied especially in the form of computer codes. In this paper, a new modification of SD method is proposed using a new search direction (dk) in the form of two parameters. Numerical results shows that this new SD has far superior convergence rate and more efficient than the classical SD method.

Identification of region of attraction for global optimization problem using interval symmetric operator

In this paper, some of the experience of the interval arithmetic methods for obtaining and locating the region of attraction of a global optimizer of a real continuous function f defined on a compact set D of R^n is described.

An interval global optimization algorithm for a class of functions with several variables

Abstract In this paper some of the ideas which have been used in an algorithm for computing and bounding the global minimizers of a twice continuously differentiable function with several variables in a given compact interval vector using interval arithmetic are described.