Nonlinear & Simulation Optimization

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Abstractions about nonlinear search, benchmark functions, selection theorems, metaheuristics, and optimization driven by simulations or interval reduction.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Golden-section search — A derivative-free interval-reduction algorithm for optimizing a unimodal function by placing interior evaluations in the golden ratio so one point can be reused each iteration.
• Griewank function — A smooth nonconvex benchmark function combining a scaled quadratic sum with a product of cosines, producing many local extrema and one standard global minimum.
• Helly's selection theorem — Every uniformly bounded sequence of monotone real functions on a compact interval has a subsequence converging pointwise, with bounded-variation generalizations providing compactness for measure and weak-convergence arguments.
• Imperialist competitive algorithm — A population-based metaheuristic that groups candidate solutions into empires whose competition, assimilation and collapse search an optimization landscape.
• Nonlinear programming — Optimization of an objective subject to constraints when the objective or at least one constraint is nonlinear in the decision variables.
• Simulation-based optimization — Optimization in which candidate decisions are evaluated by a computational simulation—often noisy, expensive and derivative-free—rather than a closed-form objective or constraint model.
• Ternary search — An interval-reduction search for the extremum of a unimodal function that compares two interior points and discards the third of the domain that cannot contain the optimum.