解约束优化问题的一类广义共轭方向法：一种几何处理

运行微分几何方法将无约束最优化中的共轭方向法推广到约束最优化问题上。在约束子流形上诱导了一类新的仿射联络使原来的约束最优化问题转化为约束流形上的无约束的局部二次规划问题。从而形成了具有广义共轭方向的一种曲搜索算法。

The Generalized Conjugate Direction Method for Constrained Optimization A Geometrical Approech

The conjugate direction method for solving the unconstrained optimization problem is extended to solving the constrained optimization problem by method of differential geomtry.By inducing a new class of affine connections on a constrained sub-manifold, the primary constrched optilnhation problem is converted to a unconstrained local quadratic programming problem.Based on the definition and construction of a new class of generalized conjugate directions, it isproved that optimum value of the primary constrained optimization problem must be located on thegeodesic line which is formed by the conjugate directions mentioned above and can be reached withinfinite searching step. Therefore a new curve search algorithm with generalized conjugate directions isput forward.