Disjunctive Programming and Piecewise Convexity: An Algorithmic Trajectory Analysis Toward Stationary Points to Avoid the Maratos Effect in Numerical Optimization

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Analyzing the framework of Disjunctive Programming and Piecewise Convexity for numerical optimization reveals several distinct perspectives, ranging from pure mathematical theory to real-world power systems engineering. The Theoretical Optimization PerspectiveThe Maratos Effect Resolution: Traditionally, optimization algorithms bypass the Maratos effect (where a good step is rejected because it temporarily increases constraint violation) using complex "watchdog" techniques or non-smooth filter methods. This framework offers a geometric alternative: flattening the constraints removes the curvature that causes the effect in the first place, allowing standard line-search or trust-region methods to achieve superlinear convergence unimpeded.Disjunctive Mechanics: By treating non-convexity as a discrete selection among convex subsets (using Boolean logic), the problem shifts from navigating rugged, non-convex terrain to traversing well-behaved, flat intersecting planes.

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