Sequential Optimality Conditions and Optimization Algorithm Termination:
The Case of the Scaled Stopping Criterion
【Abstract】
Modern continuous optimization leans heavily on optimality conditions, notably
the renowned KKT conditions. Initially introduced by Karush, these conditions
were later rediscovered and widely popularized by Kuhn and Tucker (KKT). They
serve a dual purpose: on one hand, they define good candidates for a solution,
and on the other, they act as foundational elements in the developing
optimization algorithms. Recognizing the inherent approximation nature of
sequences produced by algorithms leads naturally to sequential counterparts.
This talk will delve into this evolution, presenting its implications for
understanding the convergence of computational methods and their respective
stopping criteria. A key discussion point will be an analysis of a scaled
version of KKT, frequently employed in continuous optimization routines.