Nondifferentiable Optimization with Epsilon Subgradient Methods

Nurminski, E.A. ORCID: https://orcid.org/0000-0002-7236-6955 (1978). Nondifferentiable Optimization with Epsilon Subgradient Methods. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-78-055

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Abstract

The development of optimization methods has a significant meaning for systems analysis. Optimization methods provide working tools for quantitative decision making based on correct specification of the problem and appropriately chosen solution methods. Not all problems of systems analysis are optimization problems, of course, but in any systems problem optimization methods are useful and important tools. The power of these methods and their ability to handle different problems makes it possible to analize and construct very complicated systems. Economic planning for instance would be much more limited without linear programming techniques which are very specific optimization methods. LP methods had a great impact on the theory and practice of systems analysis not only as a computing aid but also in providing a general model or structure for the systems problems.

LP techniques, however, are not the only possible optimization methods. The consideration of uncertainty, partial knowledge of the systems structure and characteristics, conflicting goals and unknown exogenous models and consequently more sophisticated methods to work with these models.

Nondifferentiable optimization methods seem better suited to handle these features than other techniques at the present time. The theory of nondifferentiable optimization studies extremum problems of complex structure involving interactions of subproblems, stochastic factors, multi-stage decisions and other difficulties.

This publication covers one particular, but unfortunately common, situation when an estimation of the outcome from some definite decision needs a solution of a difficult auxiliary, internal, extremum problem. Solution of this auxiliary problem may be very time-consuming and so may hinder the wide analysis of different decisions. The aim of the author is to develop methods of optimal decision making which avoid direct comparison of different decisions and use only easily accessible information from the computational point of view.

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