An optimization problem subject to probabilistic (chance) constraints has the general form min{f(x)|P(g(x,ξ)≥0)≥p}, where x is a decision variable, f is an objective function, ξ is a random vector, g is a (random) constraint mapping, P refers to a probability measure and p∈(0,1) is some probability level. The inequality above (called probabilistic constraint) defines a decision x to be feasible if the random inequality system g(x,ξ)≥0 is satisfied with at least probability p. Applications of such problems are abundant in engineering, namely in power management. Traditionally, they are embedded into the area of operations research, i.e. with finite-dimensional decisions. Recently, there has been growing interest in probabilistic state constraints in PDE constrained optimization. This requires new investigations about continuity, differentiability, convexity of such problems in an infinite dimensional setting. The talk provides some recent results in this direction along with a few applications.
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