We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent ...

We consider set-valued mappings defined on a linear normed space with convex closed images in IRn. Our aim is to construct selections which are (Hadamard) directionally differentiable using some approximation of the ...

Two-stage stochastic programs with random right-hand side are considered. Optimal values and solution sets are regarded as mappings of the expected recourse functions and their perturbations, respectively. Conditions are ...

We consider multistage stochastic optimization models. Logical or integrality constraints, frequently present in optimization models, limit the application of powerful convex analysis tools. Different Lagrangian relaxation ...

We consider properties of the metric projections onto moving convex sets in normed linear spaces. Under certain conditions about the norm, directional differentiability (of higher order) of the metric projections at boundary ...

A power generation system comprising thermal and pumped-storage hydro plants is considered. Two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dynamic model for ...

We consider a new class of optimization problems involving stochastic dominance constraints of second order. We develop a new splitting approach to these models, optimality conditions and duality theory. These results are ...

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints ...

The unit commitment problem in power plant operation planning is addressed. For a real power system comprising coal- and gas-fired thermal and pumped-storage hydroplants a large-scale mixed integer optimization model for ...