The analysis of p-term algorithms for unconstrained optimization
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 1
Abstract
Consider the multidimensional unconstrained minimization problem in a case of continuously differentiable function. An iterative algorithm for solving such a problem is called a multi-term if in order to find the next approximation to the optimal point we need to compute values of the function or its gradient in two or more previous points. So that, conjugate gradient algorithm is a two-term algorithm. The aim of this paper is to study a generalized 𝑝-term method for unconstrained optimization. One substantiates the properties of this algorithm for quadratic functions and proves that it relates to conjugate direction methods. The goal of computational experiment was to compare the results of minimization with different number of terms 𝑝 and find the “optimal” value for the 𝑝. The numerical results for some well-known test functions are given.
Authors and Affiliations
Ye. M. Strakhov, A. T. Yaroviy
Keywords
Related Articles
- EP ID EP342739
- DOI -
- Views 74
- Downloads 0
Asymptotics of one class of solutions of 𝑛-th order ordinary differential equations with regularly varying nonlinearities
In the present paper the existence conditions of solutions, for each of which there exists a number 𝑘 P t3, . . . , 𝑛u such that p𝑛 _ 𝑘q-th derivative of solution tends to nonzero constant as the argument tends to 8, of...
About constant in Szego inequality for derivatives of conjugate trigonometric polynomials in L0.
We consider Szego inequality ˜ T(r) n 0 χ0 (n, r) ・ Tn 0 for derivatives of conjugate trigonometric polynomials in L0. We’ve found exact asymptotic by n estimation of constant χ0 (n, r) in it, improving estimates which...
Generalization of averaging conditions in the optimal control problem with fast and slow variables
The optimal control problem is described by the system of differential equations with fast and slow variables and by the terminal criterion of quality. There is a generalization of averaging conditions. There is proved t...
Noninvertible analogue for the congugate mapping for the pair of tent-like mappings
The functional equation which appear in the definition of the topological conjugacy of the tent-like piecewise linear mappings of an interval into itself. All the solutions of this functional equations are obtained and t...
On a two-step algorithm in structural and parametric optimization problems of linear control systems.
This paper deals with applying of a two-step optimization algorithm for structural and parametric optimization problems of linear control systems with fixed and floating switching points.