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Discrete Approximations for Strict Convex Continuous Time

Summary: Discrete Approximations for
Strict Convex Continuous Time
Problems and Duality #
R. Andreani + , P. S. Gon›calves # , and G. N. Silva §
Abstract. We propose a discrete approximation scheme to a class
of Linear Quadratic Continuous Time Problems. It is shown, under
positiveness of the matrix in the integral cost, that optimal solutions
of the discrete problems provide a sequence of bounded variation func­
tions which converges almost everywhere to the unique optimal solu­
tion. Furthermore, the method of discretization allows us to derive
a number of interesting results based on finite dimensional optimiza­
tion theory, namely, Karush­Kuhn­Tucker conditions of optimality
and weak and strong duality. A number of examples are provided to
illustrate the theory.
Key Words. Linear Quadratic problems, Continuous time opti­
mization, discrete approximation, strict convexity
# Partially supported by CNPq and FAPESP of Brasil
+ Professor, Departamento de Matem’atica Aplicada, IMECC, UNICAMP, Campinas, SP,
# Postgraduate student at Universidade de Estadual Paulista, S”ao Jos’e do Rio Preto, SP,


Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas


Collections: Mathematics