The sequential gradient-restoration algorithm (SGRA) in mathematical programming format is used to solve the mathematical programming problems of Section 6. SGRA is an iterative technique which involves a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In the gradient phase, the augmented performance index (performance index augmented by the constraints weighted via appropriate Lagrange multipliers) is decreased, while avoiding excessive constraint violation. In the restoration phase, the constraint error is decreased, while avoiding excessive change in the problem variables. In a complete gradient-restoration cycle, the performance index is decreased, while the constraints are satisfied to a preselected accuracy. Thus, a succession of feasible suboptimal solutions is generated, each new solution being an improvement over the previous one from the point of view of the performance index (25) or (27).
Note that SGRA is available in both mathematical programming format and optimal control format. For mathematical programming problems, SGRA was developed by Miele at al in both ordinary-gradient version and conjugate-gradient version ( [20]). Several variations of SGRA were also developed, but the basic form proved to be the more reliable, because of its robustness and stability properties ( [21]). For optimal control problems, the development of SGRA by Miele at al has been parallel to that for mathematical programming problems; see [22] [24] for early versions and [25] [27] for recent versions. Also for optimal control problems, an industrial version of SGRA has...
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