数学规划的物理模型及算法

利用力学原理，建立了用微分方程描述的带不等式约束优化问题的物理模型，用人工释能和摄动的思想，推广了现行的一些可行方向算法，并对算法的收敛性进行了讨论。

THE PHYSICAL MODEL AND ALGORITHMS IN MATHEMATICAL PROGRAMMING

Based on the concepts and principles of unilateral constraints in mechanics, a physical (mechanical) model with respect to general constrained optimization in forms of differential equation has been established. The relationship among equilibrium point. Lagrangian multipler in mechanics and Kuhn-Tucker point. Kuhn-Tucker multipler in mathematics has been discussed. A concise sufficient and necessary condition of Kuhn-Tucker point is also presented.The idea of "artificially release energy (ARE)" has been adopted to get a family of feasible directions by perturbing a basic direction for the general constrained nonlinear programming (GCNP). Then by way of solving the differential equation's equilibrium solution using ARE method, we get a feasible direction algorithms for GCNP. which extend some prensently known algorithms. For two given basic directions and perturbing parameters, we have proved the convergence of the corresponding algorithms without convexity constraints.