We present for the reader's attention a special issue of Applicable Analysis devoted to selected topics in modern variational analysis and its applications to various problems of optimization, equilibria, control of systems governed by ordinary differential and partial differential equations, stochastic processes, etc. Modern variational analysis has been well recognized as an active area of mathematics with the emphasis on applications. On one hand, it particularly concerns the study of optimization-related and equilibrium problems while, on the other hand, it applies variational/optimization principles as well as perturbation and approximation techniques to the analysis of a broad spectrum of problems that may not be of a variational nature. This area of applied mathematics can be treated as an outgrowth of the classical calculus of variations, optimal control theory, and constrained optimization with a special attention to sensitivity/stability analysis with respect to perturbations. Among characteristic features of modern variational analysis is a strong involvement of mathematical objects with nonstandard, nonsmooth structures (e.g., nondifferentiable functions, set with nonsmooth boundaries, and set-valued mappings), which frequently arise in the frameworks of optimization, equilibria, and systems control being in fact naturally generated by the usage of advanced variational principles and perturbation techniques. Furthermore, powerful variational principles in applied sciences (particularly in physics, mechanics, biology, and economics) also give rise to nonsmooth structures and often motivate the growth of new form of analysis. All these phenomena require the development and applications of appropriate tools of generalized differentiation.
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