An optimization algorithm for sequentially constructed problems and its stability

This paper is concerned with a new type of optimization problems, which are called ‘sequently constructed problems’. This type of problem is not completely well-defined at a point of time when an optimization algorithm starts, and is sequentially defined with the progress of the iterative algorithm. Such problems arise in an optimization approach integrated parameter identification by observation of system input/output signals. Currently used algorithm of mathematical programming, such as a descent method, is unsuitable for solution by these sequentially constructed problems, because permanence of the problem is prerequisite when the algorithm is performed. In a case when the usual method is applied unconditionally, the convergence and stability of a sequence of trial points obtained by the algorithm cannot be assured. In this paper, an algorithm for this new type of optimization problems is proposed, and sufficient conditions for stability and convergence of this algorithm are also given. [In Japanese.]