Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty

Minimax Nonlinear Control under Stochastic Uncertainty Constraints

We consider in this paper a class of stochastic nonlinear systems in strict feedback form, where in addition to the standard Wiener process there is a norm-bounded unknown disturbance driving the system. The bound on the disturbance is in the form of an upper bound on its power in terms of the power of the output. Within this structure, we seek a minimax state-feedback controller, namely one th...

Random Variational Inequalities with Applications to Equilibrium Problems under Uncertainty

In this contribution we introduce to the topic of Random Variational Inequalities (RVI) and present some of our recent results in this field. We show how the theory of monotone RVI, where random variables occur both in the operator and the constraints set, can be applied to model nonlinear equilibrium problems under uncertainty arising from economics and operations research, including migration...

Complementarity Models for Traffic Equilibrium with Ridesharing

It is estimated that 76% of commuters are driving to work alone while each of them experiences a 38-hour delay annually due to traffic congestion. Ridesharing is an efficient way to utilize the unused capacity and help with congestion reduction, and it has recently become more and more popular due to new communication technologies. Understanding the complex relations between ridesharing and tra...

Competitive Equilibrium Under Uncertainty

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Equilibrium routing under uncertainty