# 47620

## Автор(ов):

1

Параметры публикации

## Тип публикации:

Статья в журнале/сборнике

## Название:

Maximization of function with Lipschitz continuous gradient

1072-3374

## DOI:

10.1007/s10958-015-2482-6

## Наименование источника:

• Journal of Mathematical Sciences

Vol. 209, No. 1

• Москва

## Издательство:

• Plenum Publishers

2015

## Страницы:

12-18
Аннотация
In the present paper, we consider (nonconvex in the general case) functions that have Lipschitz continuous gradient. We prove that the level sets of such functions are proximally smooth and obtain an estimate for the constant of proximal smoothness. We prove that the problem of maximization of such function on a strongly convex set has a unique solution if the radius of strong convexity of the set is sufficiently small. The projection algorithm (similar to the gradient projection algorithm for minimization of a convex function on a convex set) for solving the problem of maximization of such a function is proposed. The algorithm converges with the rate of geometric progression.

## Библиографическая ссылка:

Балашов М.В. Maximization of function with Lipschitz continuous gradient // Journal of Mathematical Sciences. 2015. Vol. 209, No. 1. С. 12-18.