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Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of...
The Karush—Kuhn—Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose casting KKT systems as a minimization...
Strang  introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In  we generalized the problems and called the generalized problems...
This article considers the optimal control of nuclear fission reactors modeled by parabolic partial differential equations. The neutrons are divided into fast and thermal groups with two equations describing their interaction and fission, while a third equation describes the temperature in the...
The problem of designing a periodic interface between two materials in such a way that time-harmonic waves diffracted from the interface have a specified far-field pattern is studied.
In this paper we derive optimality conditions in the form of a maximum principle for an optimal control problem for nonlinear implicit, or descriptor, control systems. The regularity conditions which are imposed on the system allow us to reduce the optimal control problem to an equivalent...
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