集合函数多目标规划的二阶最优性条件

在给出了集合函数多目标规划的一阶最优性条件的基础上,进一步给出了集合函数多目标规划问题弱有效解的二阶充分条件和强有效解的二阶充分条件以及局部弱有效解的二阶充分条件。     

一类拟可微优化问题的最优性条件

讨论了含有一个等式约束的拟可微优化问题的最优性条件，导出了这一问题的ＦｒｉｔｚＪｏｈｎ型必要条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ型必要条件，同时给出了两个充分条件     

微生物连续培养非线性动力系统的性质及最优性条件

本文针对微生物连续发酵生产1,3-丙二醇非线性动力系统,以产物1,3-丙二醇的生产强度最大为目标泛函,建立最优控制模型。用不可微优化理论与方法证明了模型最优解的存在性与一阶最优性条件。论述了最优性函数与一阶最优性条件的等价性。     

半局部凸多目标规划的最优性条件与对偶定理

得到了半局部凸多目标规划．G-真有效解的充要条件，建立了Mond-Weir型对偶模型,证明了相应的对偶定理。     

D.C.集(凸集的差)约束的非凸二次规划的最优解集

本文研究D.C.集(凸集的差)上极小化非凸二次规划问题的最优解。我们首先证明了该问题的Lagrange对偶的稳定性,即不存在对偶间隙;接着利用该性质得到问题的全局最优性条件和最优解集,它可以像凸规划那样,借助它的对偶问题的解集精确地描述出来。最后,通过一个例子来说明这些结论。     

Zn4上完全非线性函数的存在性和构造

给出了剩余类环Z4上的逻辑函数-4值逻辑函数是完全非线性函数的两个条件，引入了布尔函数中“类Bent函数”的概念，并用其构造了自变量个数是偶数的一类4值完全非线性函数，给出了1元4值完全非线性函数不存在性的一个简单证明。     

一类不可微广义凸多目标规划的最优性条件和对偶

本文研究带不等式约束的不可微多目标规划问题,引入了广义d-I型一致不变凸函数的概念,证明了Pareto有效解和Pareto弱有效解的Karush-Kuhn-Tucker型充分条件.构造出了混合对偶模型,并证明了相应的对偶定理.     

非凸无限维规划的弱有效解

讨论了非凸无限维规划的弱有效解．其结果主要如下：广义次类凸与近次类凸条件下的Gordan择一定理；广义弱鞍点定理与Lagrange对偶；几种解之间的关系；弱有效解的必要条件与充分条件。     

Z_4~n上完全非线性函数的存在性和构造

给出了剩余类环Z4上的逻辑函数-4值逻辑函数是完全非线性函数的两个条件,引入了布尔函数中"类Bent函数"的概念,并用其构造了自变量个数是偶数的一类4值完全非线性函数,给出了1元4值完全非线性函数不存在性的一个简单证明。     

Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.     

应用编程智能处理不满幅遥感影像

遥感影像分图幅后,会出现不满幅的情况,采用其它影像填充是常用的方法。通过Photoshop编程这一方法智能填充不满幅影像,改变传统处理方法,大大提高工作效率。本文研究了Photoshop对象模型、编程语言,对不满幅影像处理的作业流程和程序实现原理进行了阐述。本文扼要说明主要部分的代码。     

求解非线性等式约束优化问题的共轭梯度投影算法

利用投影矩阵,对求解无约束规划的共轭梯度算法中的参数βk给一限制条件确定βk的取值范围,以保证得到目标函数的共轭梯度投影下降方向,建立了求解非线性等式约束优化问题的共轭梯度投影算法,并证明了算法的收敛性。数值例子表明算法是有效的。     

非线性混合整数规划问题的改进差分进化算法

针对非线性混合整数规划问题,本文采用非固定多段映射罚函数法处理约束条件、用混合整数编码技术处理连续变量和整数变量,并在基本差分进化算法中加入一种新型的凸组合变异算子和一种指数递增交叉算子,由此构造出了一种求解非线性混合整数规划问题的改进差分进化算法。实验表明,所提出的算法全局收敛速度快,精度高,鲁棒性强。     

Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.     

一类求解非线性规划的修正斜边界滤子方法

本文给出一类修正的斜边界滤子方法,结合序列二次规划方法求解非线性规划问题.我们将目标函数方向和约束违反度方向均设置了斜边界,用以构造充分减少条件.同时,和经典滤子相比,新的滤子接受试探点更加灵活,改善了迭代点的被接受机会.新的滤子也具备经典滤子的“包含性”,并被用于可行恢复项中.在较弱的条件下,可以得到全局收敛性.最后,给出了数值实验结果.     

Optimal Design of Electronic Components by Mixed-Integer Nonlinear Programming

Computer-aided design optimization of electronic components is a powerful tool to reduce development costs on one hand and to improve the performance of the components on the other. In this paper, a mathematical model of an electronic filter is outlined. It depends on certain parameters, some of them of being continuous, others of integer type. The purpose of the paper is to introduce an extension of the well-known sequential quadratic programming (SQP) method to solve the mixed-integer programming problem (MINLP). It is assumed that the integer variables cannot be relaxed to real ones, that the integer range is sufficiently large, and that they possess some physical meaning so that they basically behave like continuous ones. The general idea is to combine an SQP step with a direct search cycle in the integer space. Hessian information is updated based on difference formulae at neighbored grid points. Numerical results are included to show the feasibility of the mixed-integer nonlinear programming code for academic test examples and in addition for the optimal design of an electronic filter.     

基于工程量清单的非线性费用分摊模型

运用约束条件的非线性规划,建立起一个基于效用最大化和合理性相结合的工程量清单费用分摊模型.利用K-T条件可以求出一个经济效用的最大化,能充分考虑费用分摊的合理性的全局最优解;对解的一系列性质进行分析,发现该最优解可以使投标商在考虑合理性条件下达到经济效用最优化.该最优解可以作为最优工程量清单费用分摊标准或参考依据.