Methods of Nondifferentiable and Stochastic Optimization and Their Applications

Optimization methods are of a great practical importance in systems analysis. They allow us to find the best behavior of a system, determine the optimal structure and compute the optimal parameters of the control system etc. The development of nondifferentiable optimization, differentiable and nondifferentiable stochastic optimization allows us to state and effectively solve new complex optimization problems which were impossible to solve by classical optimization methods. The main purpose of this article is to review briefly some important applications of nondifferentiable and stochastic optimization and to characterize principal directions of research. Clearly, the interests of the author have influenced the content of this article

Global Changes: Facets of Robust Decisions

The aim of this paper is to provide an overview of existing concepts of robustness and to identify promising directions for coping with uncertainty and risks of global changes. Unlike statistical robustness, general decision problems may have rather different facets of robustness. In particular, a key issue is the sensitivity with respect to low-probability catastrophic events. That is, robust decisions in the presence of catastrophic events are fundamentally different from decisions ignoring them. Specifically, proper treatment of extreme catastrophic events requires new sets of feasible decisions, adjusted to risk performance indicators, and new spatial, social and temporal dimensions. The discussion is deliberately kept at a level comprehensible to a broad audience through the use of simple examples that can be extended to rather general models. In fact, these examples often illustrate fragments of models that are being developed at IIASA

Risk, Security and Robust Solutions

The aim of this paper is to develop a decision-theoretic approach to security management of uncertain multi-agent systems. Security is defined as the ability to deal with intentional and unintentional threats generated by agents. The main concern of the paper is the protection of public goods from these threats allowing explicit treatment of inherent uncertainties and robust security management solutions. The paper shows that robust solutions can be properly designed by new stochastic optimization tools applicable for multicriteria problems with uncertain probability distributions and multivariate extreme events

Modeling and Robust Design of Networks under Risk: The Case of Information Infrastructure

Study of network risks allows to develop insights into the methods of building robust networks, which are also critical elements of infrastructures that are of a paramount importance for the modern society. In this paper we show how the modern quantitative modeling methodologies can be employed for analysis of network risks and for design of robust networks under uncertainty. This is done on the example of important problem arising in the process of building of the information infrastructure: provision of advanced mobile data services. We show how portfolio theory developed in the modern finance can be used for design of robust provision network comprising of independent agents. After this the modeling frameworks of Bayesian nets andMarkov fields are used for the study of several problems fundamental for the process of service adoption such as the sensitivity of networks, the direction of improvements, and the propagation of user attitudes on social networks

Two stage model of ecological and economic decisions

Imperfection of ecological and economic decisions should be corrected by certain programs of public-private partnership. It is important to suggest and substantiate incentives for participation in such programs. The two-stage approach for making strategic and adaptive ecological and economic decisions is proposed