CAJ | 학술논문

考虑一类特殊的多项式整数规划问题.此类问题有很广泛的实际应用,并且是NP难问题.对于这类问题,最优性必要条件和最优性充分条件已经给出,利用这些最优性条件设计最优化算法.首先,利用最优性必要条件,给出一种新的局部优化算法.进而结合最优性充分条件、新的局部优化算法和辅助函数,设计新的全局最优化算法.给出的算例展示算法是有效的和可靠的.
고필일류특수적다항식정수규화문제.차류문제유흔엄범적실제응용,병차시NP난문제.대우저류문제,최우성필요조건화최우성충분조건이경급출,이용저사최우성조건설계최우화산법.수선,이용최우성필요조건,급출일충신적국부우화산법.진이결합최우성충분조건、신적국부우화산법화보조함수,설계신적전국최우화산법.급출적산례전시산법시유효적화가고적.
In this paper,a class of integer polynomial programming problems is considered.This class of integer polynomial programming problems has a wide range of practical applications and is NP hard.For these problems,necessary global optimality conditions and sufficient global optimality conditions have been presented recently.We will design some optimization methods to this class of integer polynomial programming problems by using these global optimality conditions.Firstly,a local optimization method is designed according to the necessary global optimality conditions for these integer polynomial programming problems.Moreover,a new global optimization method for this class of integer polynomial programming problems is presented by combining the sufficient global optimality conditions,the local optimization method and an auxiliary function.Some numerical examples are presented to illustrate the efficiency and reliability of these optimization methods.