NEW ODE METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION .2. ALGORITHMS

As a continuation of [1], this paper considers implementation of ODE approaches. A modified Hamming's algorithm for integration of (ECP)-equation is suggested to obtain a local solution. In addition to the main algorithm, three supporting algorithms are also described: two are for evaluation of the right-hand side of (ECP)-equation, which may be especially suitable for certain kinds of (ECP)-equation when applied to large scale problems; the the third one, with a convergence theorem, is for computing an initial feasible point. Our numerical results obtained by executing these algorithms on an example of (ECP)-equation given in [1] on five test problems indicate their remarkable superiority of performance to Tanabe's ODE version that is recently claimed to be much better than some well-known SQP techniques. This work is a continuation of [1], so the same notation is used as before and the section numbers are continued. Implementation problems of ODE methods are considered in detail here. In Section 4, The main algorithm, a modified Hamming's algorithm for integration of (ECP)-equation, is described. Two supporting algorithms for evaluation of the right-hand side of (ECP)-equation are presented in Section 5, which may be especially suitable for certain kinds of (ECP)-equation when applied to large scale problems. Then, in Section 6, an algorithm for computing an initial feasible point and a related convergence theorem are given. Finally, Section 7 presents our numerical results obtained by executing these algorithms on an example of (ECP)-equation proposed in [1] on five test problems. These results show their remarkable superiority of performance to Tanabe's ODE version that is recently claimed to be much better than some well-known SQP techniques[2].