多变量、多约束连续或离散的非线性规划的一个通用算法

利用目标函数对约束函数关于设计变量的一阶微分或差分之比，给出了一个求解非线性规划的通用算法．不论变量和约束有多少，也不论变量是连续的还是离散的，这一算法都比较有效，尤其对离散非线性规划更有效．该方法是一种搜索法，勿需解任何数学方程，只需要计算函数值以及函数对变量的偏微分或差分值．许多数值例题和运筹学中一些经典问题，如1) 一、二维的背包问题；2) 一、二维资源分配问题；3) 复合系统工作可靠性问题；4) 机器负荷问题等，经用此法求解验证均较传统方法更有效和可靠．该方法的主要优点是:1) 不受问题的规模限制；2) 只要在可行域（集）内存在目标函数和约束函数及其一阶导数或差分的值，肯定可以搜索到最优的解，没有不收敛和不稳定的问题．

A Universal Approach for Continuous or Discrete Non-Linear Programmings With Multiple Variables and Constraints

A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables.This approach can be efficiently used to solve continuous and,in particular,discrete programmings with arbitrary design variables and constraints. As a search method,this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables,rather than any solution of mathematic equations.The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems,one-dimensional and two-dimensional resource-distribution problems,problems of working reliability of composite systems and loading problems of machine,and more efficient and reliable solutions are obtained than traditional methods.The present approach can be used without limitation of modeling scales of the problem.Optimum solutions can be guaranteed as long as the objective function,constraint functions and their first-order derivatives/differences exist in the feasible domain or feasible set.There are no failures of convergence and instability when this approach is adopted.