Maximum and Minimum Problem of Quadratic Function of n Variables

SUN Hua-juan; HE Ai-juan; CHEN Yong-yi

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Maximum and Minimum Problem of Quadratic Function of n Variables

更新时间：2026-07-10

- Maximum and Minimum Problem of Quadratic Function of n Variables
- Vol. 17, Issue 1, Pages: 116-119(2012)
- 作者机构：
  
  1. 烟台大学文经学院
  2. 烟台大学数学与信息科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： G634.6
- Published：2012
- 稿件说明：
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SUN Hua-juan, HE Ai-juan, CHEN Yong-yi. Maximum and Minimum Problem of Quadratic Function of n Variables[J]. 2012, 17(1): 116-119.
DOI：

SUN Hua-juan, HE Ai-juan, CHEN Yong-yi. Maximum and Minimum Problem of Quadratic Function of n Variables[J]. 2012, 17(1): 116-119. DOI：

摘要

提出了n元二次函数无约束条件最值问题的一般理论和方法

得到了最大(小)值存在及最值点存在且唯一的简明的充分必要条件;有m(mn)个线性等式约束的问题可化为无约束的低维二次函数的相应问题;给出了求最大(小)值(点)的具体方法.对有非线性约束条件的问题

指出了二次型标准化方法的重要性

并举了实例.

Abstract

For maximum and minimum problem of a quadratic function of n variables without restricted conditions

we obtained both concise sufficient and necessary conditions for existence of maximum(or minimum) and existence and uniqueness of maximum(or minimum) point.The problem with m(mn) linear restricted conditions is transformed into a related problem of a quadratic function of less variables without restricted conditions.This paper gives concrete solving method for maximum and minimum.For the prob...

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