非线性l1问题的调节熵函数法

提出求解非线性l1问题的调节熵函数法．介绍了非线性l1问题的调节熵函数的有关性质、调节熵函数算法及其收敛性,最后给出数值实例．     

一类约束不可微优化问题的区间极大熵方法

本文研究求解不等式约束离散ｍｉｎｉｍａｘ问题的区间算法,其中目标函数和约束函数是 Ｃ~１类函数．利用罚函数法和极大熵函数思想将问题转化为无约束可微优化问题,讨论了极大熵函数的区间扩张,证明了收敛性等性质,提出了无解区域删除原则,建立了区间极大熵算法,并给出了数值算例．该算法是收敛、可靠和有效的．     

线性l1模极小化问题的熵函数延拓法

本文通过利用极大熵函数构造同伦映射，建立了求解无约束线性l1模问题的熵函数延拓算法，证明了方法的收敛性，并给出了数值算例．     

鲁棒稀疏重构问题的凝聚同伦算法

鲁棒稀疏重构问题是信号处理领域的重要问题,该问题的数学本质是一个NP难的数学优化问题.同伦算法是一类典型的路径跟踪算法,该算法是解非线性问题的一类成熟算法,具有全局收敛性,且易于并行实现.本文考虑同伦算法在鲁棒稀疏重构问题中的数值求解.基于l_∞范数及罚函数策略,我们首先将原始的基于l_0范数的最优化模型,转化为含参数的无约束极大极小值问题,进而构造凝聚函数光滑化模型中的极大值函数,并构造凝聚同伦算法数值求解.数值仿真实验验证了新方法的有效性,为大规模鲁棒重构问题的并行化数值求解奠定基础.     

互补问题的光滑逼近法

提出求解互补问题的一个光滑逼近法,从而可直接利用各类光滑方程组成无约束可微优化算法求解线性和非线性互补问题,数值实验表明了方法的有效性。     

非线性无约束优化问题的滤子填充函数算法

提出了一个求解无约束非线性规划问题的无参数填充函数,并分析了其性质.同时引进了滤子技术,在此基础上设计了无参数滤子填充函数算法,数值实验证明该算法是有效的.     

非线性极大极小问题一个新的QP-free算法

本文研究非线性无约束极大极小优化问题. QP-free算法是求解光滑约束优化问题的有效方法之一,但用于求解极大极小优化问题的成果甚少.基于原问题的稳定点条件,既不需含参数的指数型光滑化函数,也不要等价光滑化,提出了求解非线性极大极小问题一个新的QP-free算法.新算法在每一次迭代中,通过求解两个相同系数矩阵的线性方程组获得搜索方向.在合适的假设条件下,该算法具有全局收敛性.最后,初步的数值试验验证了算法的有效性.     

约束非线性l_1问题的光滑近似算法

针对约束非线性l_1问题不可微的特点,提出了一种光滑近似算法.该方法利用" "函数的光滑近似函数和罚函数技术将非线性l_1问题转化为无约束可微问题,并在适当的假设下,该算法是全局收敛的.初步的数值试验表明算法的有效性.     

约束非线性ι1问题的光滑近似算法

针对约束非线性ι1问题不可微的特点,提出了一种光滑近似算法.该方法利用“ “函数的光滑近似函数和罚函数技术将非线性ι1问题转化为无约束可微问题,并在适当的假设下,该算法是全局收敛的.初步的数值试验表明算法的有效性.     

N车探险问题的一种ε-近似度的近似算法

本文探讨了一类N车探险问题的近似算法,首先通过建模将N车问题转变为一个等价的非线性0-1混合整数规划问题,进而将该非线性0-1混合整数规划问题转化为一个一般的带约束非线性规划问题,并用罚函数的方法将得到的带约束非线性规划问题化为相应的无约束问题.我们证明了可通过求解该无约束非线性规划问题得到原N车问题的ε-近似度的近似解,并设计了-个收敛速度为二阶的迭代箅法,文章最后给出算法实例.     

基于动力系统的线性不等式组的解法

本文提出了一种新的求解线性不等式组可行解的方法-基于动力系统的方法．假设线性不等式组的可行域为非空,在可行域的相对内域上建立一个非线性关系表达式,进而得到一个结构简单的动力系统模型．同时,定义了穿越方向。文章最后的数值实验结果表明此算法是有效的．     

求解线性不等式组的方法

本提出了一个新的求解线性不等式组可行解的方法－－无约束极值方法。通过在线性不等式组的非空可行域的相对内域上建立一个非线性极值问题，根据对偶关系，得到了一个对偶空间的无约束极值及原始，对偶变量之间的简单线性映射关系，这样将原来线性不等式组问题的求解转化为一个无约束极值问题。中主要讨论了求解无约束极值问题的共轭梯度算法。同时，在寻找不等式组可行解的过程中，定义了穿越方向，这样大大减少计算量。中最后数值实验结果表明此算法是有效的。     

A new smoothing Newton method for solving constrained nonlinear equations

In this paper, a new smoothing Newton method is proposed for solving constrained nonlinear equations. We first transform the constrained nonlinear equations to a system of semismooth equations by using the so-called absolute value function of the slack variables, and then present a new smoothing Newton method for solving the semismooth equations by constructing a new smoothing approximation function. This new method is globally and quadratically convergent. It needs to solve only one system of unconstrained equations and to perform one line search at each iteration. Numerical results show that the new algorithm works quite well.     

基于拟态物理学的约束多目标共轭梯度混合算法

在拟态物理学优化算法APO的基础上,将一种基于序值的无约束多目标算法RMOAPO的思想引入到约束多目标优化领域中.提出一种基于拟态物理学的约束多目标共轭梯度混合算法CGRMOAPA.算法采取外点罚函数法作为约束问题处理技术,并借鉴聚集函数法的思想,将约束多目标优化问题转化为单目标无约束优化问题,最终利用共轭梯度法进行求解.通过与CRMOAPO、MOGA、NSGA-II的实验对比,表明了算法CGRMOAPA具有较好的分布性能,也为约束多目标优化问题的求解提供了一种新的思路.     

New maximum entropy-based algorithm for structural design optimization

A new algorithm based on nonlinear transformation is proposed to improve the classical maximum entropy method and solve practical problems of reliability analysis. There are three steps in the new algorithm. Firstly, the performance function of reliability analysis is normalized, dividing by its value when each input is the mean value of the corresponding random variable. Then the nonlinear transformation of such normalized performance function is completed by using a monotonic nonlinear function with an adjustable parameter. Finally, the predictions of probability density function and/or the failure probability in reliability analysis are achieved by looking the result of transformation as a new form of performance function in the classical procedure of maximum entropy method in which the statistic moments are given through the univariate dimension reduction method. In the proposed method, the uncontrollable error of integration on the infinite interval is removed by transforming it into a bounded one. Three typical nonlinear transformation functions are studied and compared in the numerical examples. Comparing with results from Monte Carlo simulation, it is found that a proper choice of the adjustable parameter can lead to a better result of the prediction of failure probability. It is confirmed in the examples that result from the proposed method with the arctangent transformation function is better than the other transformation functions. The error of prediction of failure probability is controllable if the adjustable parameter is chosen in a given interval, but the suggested value of the adjustable parameter can only be given empirically.     

一类求解非线性等式和不等式约束优化问题的区间算法

在Moore二分法的基础上,通过构造的区间列L中标志矢量R的分量取值来删除部分不满足约束条件的区域,将非线性约束优化问题转化为初始域子域上的无约束优化问题,该算法可利用极大熵方法求解多目标优化问题,理论分析和数值结果均表明,这种算法是稳定且可靠的.     

A new algorithm for total variation based image denoising

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.     

An algorithm for solving global optimization problems with nonlinear constraints

In this paper we propose an algorithm using only the values of the objective function and constraints for solving one-dimensional global optimization problems where both the objective function and constraints are Lipschitzean and nonlinear. The constrained problem is reduced to an unconstrained one by the index scheme. To solve the reduced problem a new method with local tuning on the behavior of the objective function and constraints over different sectors of the search region is proposed. Sufficient conditions of global convergence are established. We also present results of some numerical experiments.     

一类无约束离散Minimax问题的区间调节熵算法

In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C^1. The paper deals with this problem by means of taking the place of maximum-entropy function with adjustable entropy function. By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented. The relevant properties are proven, The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum-entropy algorithm. Both theoretical and numerical results show that the method is reliable and efficient.