Classical optimizer interface for hybrid algorithms

A classical optimizer interface for a hybrid algorithm is a finite classical procedure that receives a specified set of finite-precision estimates of an objective $C(\theta )$ or its derivatives, chooses the next parameter query, and terminates under a stated stopping rule with a declared output. Its interface records query precision, output encoding, classical operation/bit costs, initialization, and stopping behavior. Any convergence or sample-complexity theorem must separately state and prove assumptions such as convexity, smoothness, parameter-domain geometry, bounded noise, and initialization. A generic VQA objective is not assumed convex, and the existence of an optimizer interface supplies no rate.

This is an abstract contract: it does not select gradient descent, certify a global minimum, or provide an optimization oracle without an explicit finite procedure.