Abstract Models for the Synthesis of Optimization Algorithms

Abstract

In this paper, we present a systematic approach to the problem of synthesis of optimization algorithms. First, we develop abstract models for algorithms. These models guide the inventive process toward “conceptual” algorithms, namely, algorithms which may consist of operations that are inadmissible in a practical method (for example, a conceptual algorithm may require us to find the limit of an infinite sequence at each iteration). Once the abstract models are established, we present a set of methods for converting “conceptual” algorithms falling into the class defined by the abstract models, into "implementable" iterative procedures.