TY - JOUR

T1 - Solution of special classes of multi-extremal problems

AU - Bykadorov, Igor A.

PY - 2017

Y1 - 2017

N2 - We suggest an approach to solve special classes of multi-extremal problems to optimize the monotone combination (e.g., sum, product) of several functions, under the assumption that the effective algorithms to optimize each of this item are known (e.g., each of these functions has some properties of generalized concavity: linear fractional, etc.) The algorithm proposed is iterative. It realizes one of the idea of the branchand- bound method and consists in successive correcting of the low and the upper bounds of optimal value of objective functions. Moreover, we use the methodology of multi-objective optimization, studying the image of Pareto boundary in the image space. In each iteration, the total area of the region, guaranteed to contain the image optimal point, decreases at least twice.

AB - We suggest an approach to solve special classes of multi-extremal problems to optimize the monotone combination (e.g., sum, product) of several functions, under the assumption that the effective algorithms to optimize each of this item are known (e.g., each of these functions has some properties of generalized concavity: linear fractional, etc.) The algorithm proposed is iterative. It realizes one of the idea of the branchand- bound method and consists in successive correcting of the low and the upper bounds of optimal value of objective functions. Moreover, we use the methodology of multi-objective optimization, studying the image of Pareto boundary in the image space. In each iteration, the total area of the region, guaranteed to contain the image optimal point, decreases at least twice.

UR - http://www.scopus.com/inward/record.url?scp=85036606960&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85036606960

VL - 1987

SP - 115

EP - 122

JO - CEUR Workshop Proceedings

JF - CEUR Workshop Proceedings

SN - 1613-0073

ER -