优化问题

For static constrained multi-objective optimization problems, a new evolutionary algorithm is proposed.

给出了解带约束的静态多目标优化问题的一种新进化算法。

A new hybrid genetic algorithm was presented to handle constrained optimization.

提出了一种求解约束优化问题的混合遗传算法。

In this thesis we discuss trust region algorithms for constrained nonlinear optimization problems by three chapters.

本文主要研究约束非线性优化问题的信赖域算法，全文分为三章。

Experimental results indicate that the IPSO is robust and efficient in solving nonlinear constrained optimization problems.

对比数值实验结果表明，该算法能够有效、稳定地求解非线性约束优化问题。

In these algorithms, because of no requirements on the continuity and differentiability of the objective function, they have strong adaptability for the uncertain data and the traits of agility, strong intuitiveness and randomness; they have been put into applications broadly in a short time so as to become active approaches for solving optimization problems.

由于这些方法不要求目标函数连续可微、对计算数据的不确定性有很强的适应能力，且具有灵活性好、直观性和随机性强等特点，因此在很短的时间内就得到了广泛应用，成为解决优化问题的一种有力工具，并展示出方兴未艾的强劲发展势头。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

To solve continuous function optimization problems, a new stochastic search algorithm based on ant swarm intelligence is introduced .

引言蚁群算法是最近几年才提出的一种新型的模拟进化算法，2000年把蚁群算法扩展到了求解连续函数的优化问题[1]。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

And its convergence property, asymptotically converges in probability, is proved. Numerical results on some typical optimization problems show that the algorithm proposed is efficient.

数值结果表明，对于维数较高的连续函数优化问题，采用基于均匀分布的进化策略能够快速有效地收敛到全局极小点。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新