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A general Hamilton-Jacobi framework for non-linear state-constrained control problems

Albert Altarovici, Olivier Bokanowski, Hasnaa Zidani (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can always be described...

A Generalization of Dynamic Programming for Pareto Optimization in Dynamic Networks

Teodros Getachew, Michael Kostreva, Laura Lancaster (2010)

RAIRO - Operations Research

The Algorithm in this paper is designed to find the shortest path in a network given time-dependent cost functions. It has the following features: it is recursive; it takes place bath in a backward dynamic programming phase and in a forward evaluation phase; it does not need a time-grid such as in Cook and Halsey and Kostreva and Wiecek's "Algorithm One”; it requires only boundedness (above and below) of the cost functions; it reduces to backward multi-objective dynamic programming if there are...

A generalized proximal point algorithm for the nonlinear complementarity problem

Regina S. Burachik, Alfredo N. Iusem (2010)

RAIRO - Operations Research

We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in Rn. It differs from the classical proximal point method discussed by Rockafellar for the problem of finding zeroes of monotone operators in the use of generalized distances, called φ-divergences, instead of the Euclidean one. These distances play not only a regularization role but also a penalization one, forcing the sequence generated by the method to remain in the...

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