Comparison of Several Gradient Algorithms for Mathematical Programming Problems
RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP
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In the paper, the numerical solution of the basic problem of mathematical programming is considered. This is the problem of minimizing a function fx subject to a constraint phix 0. Here, f is a scalar, x an n- vector, and phi a q-vector, with qn. Six variations of the sequential gradient-restoration algorithm and the combined gradient-restoration algorithm are considered, and their relative efficiency in terms of number of iterations for convergence is evaluated. The variations being considered are as follows i SGRA-CR, sequential gradient-restoration algorithm, complete restoration, ii SGRA-IR, sequential gradient-restoration algorithm, incomplete restoration, iii SGRA-OR, sequential gradient-restoration algorithm, optional restoration, iv CGRA-NR, combined gradient-restoration algorithm, no restoration, v CGRA- AR, combined gradient-restoration algorithm, alternate restoration, vi CGRA- OR, combined gradient-restoration algorithm, optional restoration.
- Operations Research