Scaling of Symmetric Rank One Method in Solving Unconstrained Optimization Problem

In: Science

Submitted By nemoz3122
Words 2895
Pages 12
CHAPTER 1
INTRODUCTION

Background Of the Study

In mathematics, optimization problem is a problem where it consists of maximizing or minimizing a real function by systematically choose an input values within an allowed set and compute the value of the function. An additional, it also means solve the problem so that we can the goal as quickly as possible without wasting a lot of resources.

Optimization also can be deviating from a target by the smallest possible margin. Generally, a large area of applied mathematics is comprised by the optimization theory and techniques to other formulations. In the simple case, optimization is like finding a good value or a best available value of some problems given a defined domain, including a many of different types of objectives functions and different types of domains.

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the scalar field, and whose the magnitude is that rate of increase. The variation in space of any quantity can be represented by a slope in simple terms. The gradient is like represents the steepness and the direction of the slope. The gradient or gradient of a scalar function f〖:R〗^n→R^1 is denoted by ∇f or ∇ ⃗f where ∇ denotes the vector of the differential operator.

Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and this matrix is later named after him. Hessian matrix is the matrix of second derivatives of a multivariate function. In mathematics it means the gradient of the gradient of a function. Hessian matrix is relevant in many places such as in economy too.

Let a real-valued function f〖:R〗^n→R^1 be given and if all the second partial derivatives of f exist and are continuous over the domain of the function, then the Hessian matrix of f is

H(f)_ij (x)=D_i D_j f(x)=(δ^2…...

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