Limitsseek

Limitsseek is a framework and algorithmic approach for identifying limit points, saturation bounds, or asymptotic capacities of mathematical models and computational systems. It focuses on limit-driven exploration of parameter spaces, aiming to locate parameter values at which system behavior stabilizes, becomes infeasible, or crosses a defined threshold.

Method: It starts with broad sampling of the input domain, detects signals that a boundary is approached, and then concentrates the search near suspected limits. It uses monotonicity, Lipschitz information, or derivatives when available to guide extrapolation, and applies pruning to discard regions unlikely to yield new limits.

Applications: It is used in numerical analysis to locate convergence limits of sequences, in optimization to identify parameter bounds, in control theory to map feasible operating regions, and in benchmarking to assess ultimate system performance under stress.

Variants and relationships: Limitsseek exists in deterministic and stochastic forms, for discrete or continuous spaces, and can be integrated with Bayesian optimization, branch-and-bound, or derivative-free methods. It relates to asymptotic analysis and global optimization.

Origin and usage: The term emerged in optimization and numerical analysis literature in the 2010s as a descriptive label for limit-oriented search strategies. It denotes a family of approaches rather than a single standardized algorithm.