[分化][數] 約束優化；[分化][數] 有約束優化
In this paper, a kind of general constrained optimization problem is discussed.
在本文中，我們讨論的是一般約束優化的問題。
In this paper, we consider the nonlinear inequality constrained optimization problems.
在本文中，我們考慮非線性不等式約束優化問題。
Using the idea of both ant colony optimization algorithm and particle swam optimization algorithm, a continuous domains ant colony algorithm for solving constrained optimization problem was proposed.
借鑒蟻群優化算法和粒子群優化算法的思想，提出了一種用于求解約束優化問題的連續域蟻群算法。
In this paper, a trust region method with new conic model for linearly constrained optimization problems is proposed.
本文提出了一個解線性等式約束優化問題的新錐模型信賴域方法。
After translating constrained optimization problem into unconstrained optimization problem with penal function method, solve mathematical modal by method of coordinate rotation.
用懲罰函數法把約束優化問題轉化為無約束優化問題，以坐标輪換法進行求解。
A subspace truncated-Newton algorithm for large-scale bound constrained optimization is proposed.
給出了大規模界約束優化的一個子空間截斷牛頓法。
After discussing economic emission load dispatch, which belongs to multi-objective constrained optimization problem, the main process of solving this problem by immune genetic algorithm is given.
讨論環境經濟負荷調度多目标函數優化問題，給出利用免疫遺傳算法解決這一問題的主要步驟。
In this paper, we develop a trust region algorithm for convex constrained optimization problems.
本文我們考慮求解凸約束優化問題的信賴域方法。
In this paper we construct a new evolutionary strategies for solving constrained optimization problems.
構造了求解非線性約束優化問題的雜交進化策略。
Sequential Unconstrained Minimization Techniques (SUMT) are most common and comparatively successful method in constrained optimization.
罰函數法（SUMT）是處理約束優化問題時最常用、也是較為成功的一種方法。
Therefore, its KKT conditions are different from those of the general equality constrained optimization problem.
轉化後的問題要求其乘子是非負的，故其KKT條件與一般的等式約束優化問題不同。
The sequence quadratic programming method, i. e. , SQP method, is a well-known method for solving constrained optimization.
著名的序列二次規劃方法，簡稱SQP方法，是求解非線性約束優化問題的一類非常重要的方法。
Some sufficient conditions for a KKT point of the constrained optimization problem to be a solution of GNCP are presented.
對于廣義互補問題，本文給出了它的約束優化問題的兩種轉化形式，讨論了它們的KKT點為原問題的解的充分條。
Novel constrained optimization evolutionary algorithm based on self-adaptive good points set(COEAAGP) is proposed to tackle constrained optimization problems(COPs) in this paper.
提出一種用于求解約束優化問題的自適應佳點集進化算法。
The Optimal design of electronic circuits is a problem of constrained optimization.
電子電路的優化設計是非線性約束優化問題。
A hybrid algorithm, PSODE, is proposed by combining particle swarm optimization (PSO) with different evolution (DE), for solving constrained optimization problems.
一種混合算法，PSODE，提出了不同的進化（DE），用于求解約束最優化問題的粒子群優化（PSO）相結合。
Constrained optimization evolutionary algorithm based on memory, which integrates particle swarm optimization (PSO) with differential evolution (DE), named MCOEA, is proposed.
本文作者還結合記憶策略、差異進化算法和粒子群優化算法提出記憶進化算法（MCOEA）。
Constrained optimization problems (COPs) belong to a kind of mathematical programming problem, which is frequently encountered in the disciplines of science and engineering application.
在科學研究和工程實踐中，許多實際問題最終都歸結為求解一個帶約束條件的函數優化問題。
The model is solved by the method of nonlinear constrained optimization.
進而采用非線性約束優化方法求解模型。
Penalty function was added to system-level object function to convert unconstrained optimization into constrained optimization.
增加系統級罰函數，使系統級優化問題轉化為無約束優化問題；
We start from method development for the general nonlinear constrained optimization.
論文的第一部分是關于一般約束的非線性優化問題。
PSO algorithm; chaotic particle swarm optimization algorithm; constrained optimization; penalty function;
PSO算法；混沌粒子群算法；約束優化；懲罰函數；
In this paper, we are concerned with the sequence quadratic programming (SQP) methods for solving constrained optimization problems.
利用二次規劃技術，給出線性約束最優化問題的一個超線性收斂的可行方向法。
A class of Broyden methods for LC1 constrained optimization problems are presented and the global convergence for this class of methods is discussed when the objective function is convex.
提出了一種求解LC1類約束優化問題的拟牛頓（Broyden）族算法，在假設目标函數是凸的LC1類函數的情況下，證明了該算法的全局收斂性。
In this paper, We prove the existence of a weak minimum for constrained vector optimization problem by ****** use of vector variational-like inequality and semi-preinvex functions.
本文通過使用向量似變分不等式和半預不變凸函數來證明約束向量優化的弱極小值的存在性。
約束優化（Constrained Optimization）是數學優化領域中的一個核心分支，指在滿足一組特定限制條件（約束）的前提下，尋找目标函數最優值（最大值或最小值）的過程。它在工程、經濟學、運籌學、機器學習等領域具有廣泛應用，用于解決資源有限條件下的最佳決策問題。
以下是詳細解釋：
核心概念
數學形式化表達 一個标準的約束優化問題可以表述為： $$ begin{align} min_{mathbf{x} in mathbb{R}^n} quad & f(mathbf{x}) text{subject to} quad & g_i(mathbf{x}) leq 0, quad i = 1, ldots, m & h_j(mathbf{x}) = 0, quad j = 1, ldots, p end{align} $$ 其中：
應用價值 約束優化解決了現實世界中普遍存在的資源受限問題：
主要類型與求解方法
求解思路
約束優化是尋找在給定限制條件下最佳解決方案的數學框架。它通過形式化定義目标（需優化什麼）和約束（必須滿足的條件），為跨學科領域的複雜決策問題提供了系統化和量化的解決途徑。其核心挑戰在于如何在可行域内高效地找到全局最優解或高質量的可行解。
參考來源：
Constrained Optimization（約束優化） 是數學和運籌學中的一個核心概念，指在滿足特定限制條件（約束）的前提下，尋找目标函數的最優解（最大值或最小值）。以下是詳細解釋：
假設需最小化成本函數 $f(x) = x$，且滿足約束 $x geq 1$。
解：可行域為 $x geq 1$，最優解在 $x=1$ 處，此時 $f(x)=1$。
若需進一步了解具體算法或應用案例，可參考運籌學教材或數學優化相關資源。
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