Search Direction Generation via a Proposed Model

Abstract

This study proposes a decomposition method through which they can be a successful solution to multi-stage stochastic nonlinear programs. The proposed method entails the scenario analysis method. The proposed method also performs its role via search direction generation in such a way that sets of quadratic programming sub-issues are solved in a parallel way, especially when the size is significant lower, compared to the case involving original problems at the respective iterations. Relative to the dual multiplier derivation, which focuses on non-anticipativity constraints, the proposed system advocates for the introduction of generalized reduced gradient approaches. This study’s focus is on the efforts seeking to establish a nonlinear programming model targeting problems with much nonlinearity, as well as linear constraints existing in large sparse sets; with the objective function on the focus. From experience, most of the linear programming issues are large (inordinately) because of their attempt towards approximation via piecewise linearization, translating into nonlinear issues. Also, most of the problems in the real-world have fewer variables linked to the objective function’s nonlinearity.