# Stochastic Quasigradient (SQG) methods: Applications

Stochastic Quasi-Gradient (SQG) methods have been developed for solving general optimization problems without exact calculation of objective function and constraints (let alone of their derivatives). SQG methods enable a sequential revision of approximate solutions towards the optimal using newly acquired information on the system, obtained via either direct on-line observations or(and) simulations.

Thus, SQG methods combine simulation models and (stochastic) optimization procedures in a single decision-making framework. SQG methods can be used in a wide range of practical problems, which are difficult or impossible to be solved by traditional optimization approaches. There are at least three main application areas for SQG methods:

• Deterministic problems for which the calculation of descent directions is difficult or even impossible (large scale, non-smooth, distributed, and nonstationary optimization models)
• Multi-extremal problems where it is important to bypass local solutions.
• SQG can solve stochastic optimization problems when probability distribution functions of stochastic variables are analytically intractable. In particular, they can depend on decisions of various agents (endogenous or systemic risk). These problems involve non-smooth functions, e.g. such as nested stochastic minmax performance indicators, probabilistic solvency, reliability and security constraints, VaR and CVaR risk measures. In contrast to traditional optimization methods, SQG does not require the exact evaluation of the functions and their sub-gradients (stochastic, spatial, and dynamic optimization problems with multidimensional integrals, simulation and other analytically intractable models), which is usually difficult and even impossible.

SQG methods solve in an iterative way, thus requiring modest computer resources allocated per iteration, and reach with reasonable speed the vicinity of optimal solutions, with an accuracy that is sufficient for many application.

The implementation of the method is available on request.

On-going SQG-related research activities

Robust food-energy-water-land use NEXUS management for sustainable development: ASA, ESM, ENE, WAT develop new SQG-based approaches for iterative linkage of distributed models under uncertainty and asymmetric information to derive robust integrative solutions across sectors and regions.

Robust Disaster Risk Reduction (rDRR) mechanisms: A joint research initiative between IIASA RAV, ASA, and ESM Programs focuses on the development of SQG-based optimization approach for the design of optimal and robust disaster risk management financing programs. The optimization models are intended to be used to advise developing countries regarding better allocation of fiscal resources across different risk reduction and transfer instruments.

Simulation and optimization of stochastic (SOS_Water) water resource management: IIASA cross-program initiative between ASA, WAT, and ESM develops novel methods combining simulation and stochastic optimization for optimal and robust water-food-energy-environmental NEXUS management under uncertainty and resource scarcity.

Recent SQG-based models:

Integrated Catastrophe Risk Management (CRIM) Model

Both models are available on request.

Last edited: 24 March 2021

CONTACT DETAILS

Yurii Yermoliev

Emeritus Research Scholar Cooperation and Transformative Governance Research Group - Advancing Systems Analysis Program

Emeritus Research Scholar Exploratory Modeling of Human-natural Systems Research Group - Advancing Systems Analysis Program

T +43(0) 2236 807 208

CONTACT DETAILS

Tatiana Ermolieva

Research Scholar Integrated Biosphere Futures Research Group - Biodiversity and Natural Resources Program

T +43(0) 2236 807 581

Taher Kahil

Research Group Leader and Research Scholar Water Security Research Group - Biodiversity and Natural Resources Program

T +43(0) 2236 807 325

Junko Mochizuki

Research Scholar Water Security Research Group - Biodiversity and Natural Resources Program

T +43(0) 2236 807 576

PUBLICATIONS

Ermoliev, Y. (2009). Stochastic quasigradient methods. In: Encyclopedia of Optimization. Eds. Floudas, C.A. & Pardalos, P.M., New York: Springer-Verlag. ISBN 978-0-387-74758-310.1007/978-0-387-74759-0_662.

Ermoliev, Y. (2009). Stochastic quasigradient methods in minimax problems. In: Encyclopedia of Optimization. Eds. Floudas, C.A. & Pardalos, P.M., New York: Springer-Verlag. ISBN 978-0-387-74758-310.1007/978-0-387-74759-0_664.

Ermoliev, Y. (2009). Stochastic quasigradient methods: Applications. In: Encyclopedia of Optimization. Eds. Floudas, C.A. & Pardalos, P.M., New York: Springer-Verlag. ISBN 978-0-387-74758-310.1007/978-0-387-74759-0_663.

PUBLICATIONS

Ermoliev, Y., Ermolieva, T., Fischer, G., , Nilsson, S., & (2008). Discounting, catastrophic risks management and vulnerability modeling. Mathematics and Computers in Simulation 79 (4), 917-924. 10.1016/j.matcom.2008.02.004.

Ermolieva, T. & Ermoliev, Y. (2005). Catastrophic risk management: flood and seismic risks case studies. In: Applications of Stochastic Programming. Eds. Wallace, S.W. & Ziemba, W.T., Philadelphia: MPS-SIAM Series on Optimization.

International Institute for Applied Systems Analysis (IIASA)
Schlossplatz 1, A-2361 Laxenburg, Austria
Phone: (+43 2236) 807 0 Fax:(+43 2236) 71 313