Iterative solution procedure for nonsmooth nondifferentiable stochastic optimization: linking distributed models for food, water, energy security nexus management

Ermoliev, Y., Zagorodniy, A.G., Bogdanov, V.L., Ermolieva, T., Havlik, P. ORCID: https://orcid.org/0000-0001-5551-5085, Rovenskaya, E. ORCID: https://orcid.org/0000-0002-2761-3443, Komendantova, N. ORCID: https://orcid.org/0000-0003-2568-6179, & Obersteiner, M. ORCID: https://orcid.org/0000-0001-6981-2769 (2021). Iterative solution procedure for nonsmooth nondifferentiable stochastic optimization: linking distributed models for food, water, energy security nexus management. In: 31st European Conference on Operational Research, 11-14 July, 2021, Athens, Greece.

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Abstract

Detailed sectorial and regional models have traditionally been used for planning developments of respective sectors and regions. However, solutions that are optimal for a sub-system may turn out to be infeasible for the entire system. In this talk, we discuss a new modelling approach enabling the linkage of detailed distributed models of subsystems under joint resource constraints, uncertainty, systemic risks, and asymmetric information. The approach is based on a Stochastic Quasigradient (SQG) iterative solution procedure for nonsmooth nondierentiable optimization problems. The models are linked in a decentralized fashion via a central planner (central "hub") without requiring the exact information about models’ structure and data, i.e. in the conditions of asymmetric information and uncertainty. The sequential SQG solution procedure organizes an iterative computerized negotiation between sectorial (food, water, energy, environmental) systems (models) representing Intelligent Agents. The convergence of the procedure to the socially optimal solution is based on the results of nondifferentiable optimization providing a new type of machine learning algorithms. The linkage problem can be viewed as a general endogenous reinforced learning problem of how software agents (models) take decisions in order to maximize the "cumulative reward". The approach is illustrated by linking distributed agricultural, water and energy sector models for food-water-energy nexus security.

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