Abstract:This paper introduces new hybrid algorithm between BFGS update of Hessian matrix in Quasi-Newton methods and coefficient conjugate of BZAU in CG methods. The convergence of hybrid algorithm has been proved by sufficient descent condition. In the end of this paper, numerical results demonstrate efficiency of new algorithm on standard test problems from previous studies.

Keywords:Unconstrained Optimization, Quasi-Newton algorithms, CG algorithms, BFGS update.
Title: Novel Hybrid Algorithm in Solving Unconstrained Optimizations Problems
Author: Ziad Khanaiah, Gfr Hmod
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract:The aim of this paper is to study and generalize some results and properties with the Moreau-Yosida function of one variable for convex functions to the Moreau-Yosida function of two variables for convex-concave functions. And studing the convergenc of Moreau-Yosida sequence functions according to the concept of Mosco-epi/hypo graph and Housdorff distance in reflixive Banach spaces.

Keywords:epi-graph, optimization problems, convex-concave functions, Moreau-yosida distance, parent functions, Mosco-epi/hypo-graph.
Title: On the convergence of sequences of the Moreau-yosida function with tow variables in the reflixive Banach spaces
Author: Soueycatt Mohamed, Ali Wadih, Ali Moualla
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals
 

Abstract: Scientific forecasting depends on mathematical modelling and statistical modelling. Mathematical models are deterministic, therefore mathematical models are unable to capture the uncertainty in real life. Statistics is known as mathematics of uncertainty. Statistical models contain the randomness; therefore statistical models have become more prominent in forecasting. The theory of Uniform Circular Motion introduced several mathematical models to describe the motion of a particle in a horizontal or vertical circle. These models were extensively used in the fields of Physics and Engineering, but rarely in the fields of Economics, Finance, and Management etc. Yet, in recent past, the theory of Uniform Circular Motion was incorporated with Statistics in forecasting risk and return of Sri Lankan share market. The models developed to measure the return and risk were named as; Circular Model (CM) and Circular Indicator (CI) respectively. Share trading is important to the investors, industries as well as the entire economy of a country. In general, share market investments are high return, but high risk too. A portfolio is a combination of risky assets, which is deem to minimize the risk and maximize the profit. In modern portfolio theory, total risk of a portfolio is measured by the variance, but the variance is not a suitable measurement for time series data, as they are not independent. This study was focused on combining the CM and CI to develop a Statistical Indicator to give useful information to investors in portfolio selections. Suggested Indicator; named as Coefficient of Stability (CoS) was tested on Sri Lankan share market.

Keywords: Circular model, Circular Indicator, Mathematical Modelling, Statistical Modelling.
Title: THEORY OF UNIFORM CIRCULAR MOTION IN PORTFOLIO SELECTION
Author: W. G. S. Konarasinghe
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract:The Minimum Cost Flow (MCF) Problem is to send flow from a set of supply nodes, through the arcs of a network, to a set of demand nodes, at minimum total cost, and without violating the lower and upper bounds on flows through the arcs .
In this paper, we will illustrate an implementation of network simplex method (big-M)version for a variant of MCF.
Network simplex method (N.S.A) is one of the most popular and effective solution methods for (MCF) problem in practice. It maintains a basic feasible solution and gradually improves its objective function value by small transformations, called pivots.
We will consider four pivot rules and compare their features .
Keywords:Minimum Cost Flow , Network flow , Network Optimization , Network Simplex (big-M), Pivot rules , Strongly feasible tree .
Title: An Implementation of Network Simplex Method (Big-M) for solving Minimum Cost Flow Problem
Author: Dr. Mohammad Hassan Hassan, Farah Ghalawingy
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals