[分化][数] 约束优化；[分化][数] 有约束优化
In this paper, a kind of general constrained optimization problem is discussed.
在本文中，我们讨论的是一般约束优化的问题。
In this paper, we consider the nonlinear inequality constrained optimization problems.
在本文中，我们考虑非线性不等式约束优化问题。
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.
借鉴蚁群优化算法和粒子群优化算法的思想，提出了一种用于求解约束优化问题的连续域蚁群算法。
In this paper, a trust region method with new conic model for linearly constrained optimization problems is proposed.
本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法。
After translating constrained optimization problem into unconstrained optimization problem with penal function method, solve mathematical modal by method of coordinate rotation.
用惩罚函数法把约束优化问题转化为无约束优化问题，以坐标轮换法进行求解。
A subspace truncated-Newton algorithm for large-scale bound constrained optimization is proposed.
给出了大规模界约束优化的一个子空间截断牛顿法。
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.
讨论环境经济负荷调度多目标函数优化问题，给出利用免疫遗传算法解决这一问题的主要步骤。
In this paper, we develop a trust region algorithm for convex constrained optimization problems.
本文我们考虑求解凸约束优化问题的信赖域方法。
In this paper we construct a new evolutionary strategies for solving constrained optimization problems.
构造了求解非线性约束优化问题的杂交进化策略。
Sequential Unconstrained Minimization Techniques (SUMT) are most common and comparatively successful method in constrained optimization.
罚函数法（SUMT）是处理约束优化问题时最常用、也是较为成功的一种方法。
Therefore, its KKT conditions are different from those of the general equality constrained optimization problem.
转化后的问题要求其乘子是非负的，故其KKT条件与一般的等式约束优化问题不同。
The sequence quadratic programming method, i. e. , SQP method, is a well-known method for solving constrained optimization.
著名的序列二次规划方法，简称SQP方法，是求解非线性约束优化问题的一类非常重要的方法。
Some sufficient conditions for a KKT point of the constrained optimization problem to be a solution of GNCP are presented.
对于广义互补问题，本文给出了它的约束优化问题的两种转化形式，讨论了它们的KKT点为原问题的解的充分条。
Novel constrained optimization evolutionary algorithm based on self-adaptive good points set(COEAAGP) is proposed to tackle constrained optimization problems(COPs) in this paper.
提出一种用于求解约束优化问题的自适应佳点集进化算法。
The Optimal design of electronic circuits is a problem of constrained optimization.
电子电路的优化设计是非线性约束优化问题。
A hybrid algorithm, PSODE, is proposed by combining particle swarm optimization (PSO) with different evolution (DE), for solving constrained optimization problems.
一种混合算法，PSODE，提出了不同的进化（DE），用于求解约束最优化问题的粒子群优化（PSO）相结合。
Constrained optimization evolutionary algorithm based on memory, which integrates particle swarm optimization (PSO) with differential evolution (DE), named MCOEA, is proposed.
本文作者还结合记忆策略、差异进化算法和粒子群优化算法提出记忆进化算法（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.
在科学研究和工程实践中，许多实际问题最终都归结为求解一个带约束条件的函数优化问题。
The model is solved by the method of nonlinear constrained optimization.
进而采用非线性约束优化方法求解模型。
Penalty function was added to system-level object function to convert unconstrained optimization into constrained optimization.
增加系统级罚函数，使系统级优化问题转化为无约束优化问题；
We start from method development for the general nonlinear constrained optimization.
论文的第一部分是关于一般约束的非线性优化问题。
PSO algorithm; chaotic particle swarm optimization algorithm; constrained optimization; penalty function;
PSO算法；混沌粒子群算法；约束优化；惩罚函数；
In this paper, we are concerned with the sequence quadratic programming (SQP) methods for solving constrained optimization problems.
利用二次规划技术，给出线性约束最优化问题的一个超线性收敛的可行方向法。
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.
提出了一种求解LC1类约束优化问题的拟牛顿（Broyden）族算法，在假设目标函数是凸的LC1类函数的情况下，证明了该算法的全局收敛性。
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.
本文通过使用向量似变分不等式和半预不变凸函数来证明约束向量优化的弱极小值的存在性。
约束优化（Constrained Optimization）是数学优化领域中的一个核心分支，指在满足一组特定限制条件（约束）的前提下，寻找目标函数最优值（最大值或最小值）的过程。它在工程、经济学、运筹学、机器学习等领域具有广泛应用，用于解决资源有限条件下的最佳决策问题。
以下是详细解释：
核心概念
数学形式化表达 一个标准的约束优化问题可以表述为： $$ begin{align} min_{mathbf{x} in mathbb{R}^n} quad & f(mathbf{x}) text{subject to} quad & g_i(mathbf{x}) leq 0, quad i = 1, ldots, m & h_j(mathbf{x}) = 0, quad j = 1, ldots, p end{align} $$ 其中：
应用价值 约束优化解决了现实世界中普遍存在的资源受限问题：
主要类型与求解方法
求解思路
约束优化是寻找在给定限制条件下最佳解决方案的数学框架。它通过形式化定义目标（需优化什么）和约束（必须满足的条件），为跨学科领域的复杂决策问题提供了系统化和量化的解决途径。其核心挑战在于如何在可行域内高效地找到全局最优解或高质量的可行解。
参考来源：
Constrained Optimization（约束优化） 是数学和运筹学中的一个核心概念，指在满足特定限制条件（约束）的前提下，寻找目标函数的最优解（最大值或最小值）。以下是详细解释：
假设需最小化成本函数 $f(x) = x$，且满足约束 $x geq 1$。
解：可行域为 $x geq 1$，最优解在 $x=1$ 处，此时 $f(x)=1$。
若需进一步了解具体算法或应用案例，可参考运筹学教材或数学优化相关资源。
fluMount Qomolangmayoghurtelectromagnetic spectrumon the basis ofbecloudCTfoetusesHUAimbibitionottersskillingunfulfilledbreathing spacedark adaptationdental pulpexpand intoknocking outmolten steelporous mediaunder a cloudwater cannonchecklesscytologistDEXdiadromousdichloronitrobenzeneEuronetindefensibilityextremely low frequency