Investigation of Problems Leading to Global Extrema

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F13%3A00497670" target="_blank" >RIV/60162694:G43__/13:00497670 - isvavai.cz</a>

Result on the web

<a href="http://vavtest.unob.cz/registr" target="_blank" >http://vavtest.unob.cz/registr</a>

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Investigation of Problems Leading to Global Extrema

Original language description

In many situations, the best solutions of some problems are to be found. The problems are usually replaced by their mathematical models and become mathematical problems. The branch of mathematics studying this topic is theory of optimization. In this contribution we concentrate on the investigation of problems modelled by real functions of several variables. In this case, finding the best solution means to determine global extrema of an objective function. The situation simplifies substantially if it is known that global extrema exist. Then it is sufficient to find critical points, i.e. points in which local extrema can occur, to decide whether they are points of local extrema and choose those giving the greatest or smallest value. The standard result guaranteeing the existence of global extrema is the well-known Weierstrass Theorem: Any function continuous on a compact domain assumes its greatest and smallest value. The situation complicates when the existence of global extrema is not guaranteed. There are no universal methods how to proceed in such cases. In the paper, a few possible approaches are presented and their use on examples is demonstrated. They include namely solutions based on monotonicity and some important inequalities. Likewise their efficiency and the comparison with standard tools of differential calculus for functions of several variables for finding local extrema (first and second order conditions) are discussed.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

ICERI2013 Proceedings

ISBN

978-84-616-3847-5

ISSN

2340-1095

e-ISSN

—

Number of pages

6

Pages from-to

4745-4750

Publisher name

IATED Digital Library

Place of publication

Sevilla, Spain

Event location

Sevilla, Spain

Event date

—

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000347240604120