FminPE

FminPE stands for Fminimization with Partial Evaluation, a term used to describe a family of numerical optimization approaches that integrate partial evaluation techniques with traditional gradient-based search. The aim is to minimize nonlinear objective functions, often with simple bound constraints, while reducing the number of expensive function evaluations.

The core idea of FminPE is to reuse and memoize computations within and across function evaluations. By identifying reusable subexpressions and leveraging cached values for nearby iterates, the method seeks to accelerate convergence when objective evaluations are costly. In practice, FminPE combines a gradient-based search (such as quasi-Newton or conjugate gradient directions) with a line search or trust-region framework. Partial evaluation is implemented through caching, expression simplification, and exploiting problem structure to avoid redundant work.

Constraints are typically handled by standard techniques such as penalty methods, augmented Lagrangian formulations, or simple projection onto feasible sets. The resulting algorithms can operate in unconstrained form when appropriate, or in constrained form with fidelity to variable bounds and other restrictions.

Convergence properties of FminPE depend on the smoothness and structure of the objective. Under common assumptions, local convergence to stationary points can be established; global convergence is not guaranteed for nonconvex problems. The practical performance of FminPE is highly problem-dependent and is most advantageous when objective evaluations are expensive or when the problem contains exploitable structure.

In literature and teaching contexts, FminPE is described as a conceptual framework rather than a single standardized solver. It informs the design of hybrid methods that blend evaluation efficiency with robust gradient-based optimization, and is applicable to engineering, parameter estimation, and scientific computing where expensive objective evaluations arise.