The Hahn Quantum Variational Calculus

Details The Hahn Quantum Variational Calculus The Hahn Quantum Variational Calculus

2010-06-18

arxiv.org/abs/1006.3765v1

J. Optim. Theory Appl. 147 (2010), no. 3, 419--442

Mathematics

Optimization and Control

Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory

Scientific paper

10.1007/s10957-010-9730-1

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.

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