Relevant Theories and Numerical Methods of Curvilinear Search

Abstract:

      Some various ordinary differenrial equations are uniformly expressed to describe descending curves of the nonconstrained optimization problem. Two common seen equations are proven to illustrate an identical curve which are with different parameters essentially. A kind of the equations is proposed and is proven to be available for the numerical calculation. We also propose two algorithms-the search based on integrations and the additional inerpolution. Investigations shows that strategies of the curvilinear search and rensing iterative information may increase the efficiency and the stability of optimization algorithms.