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Complexity of Optimal Paths in Strongly Concave Problems

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Nonlinear Dynamics in Economics and Social Sciences

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 399))

Abstract

Several economic problems are often formulated in terms of a dynamic optimization model. Although a broad variety of mathematical models have been studied, the optimal capital accumulation model originated in Ramsey (1928) has played a prominent role. From the mathematical point of view, it can be formulated as a discrete-time, infinite-horizon concave optimization problem:

$$\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{{W}_{\delta }}({{x}_{0}}) = {{{\sup }}_{{({{x}_{t}})}}}\sum _{{t = 0}}^{\infty }V({{x}_{t}},{{x}_{{t + 1}}}){{\delta }^{t}}} & {s.t.} \\ \end{array} } \hfill \\ {({{x}_{t}},{{x}_{{t + 1}}}) \in D and {{x}_{0}} is fixed,} \hfill \\ \end{array}$$
(P)

where V:D → R is a concave function defined over a convex and closed set D ⊂ X × X, and the initial condition x 0 belongs to X = pr1 (D) ⊂ Rn.

This research was partially supported by M.U.R.S.T. “National Group on Non-Linear Dynamics in Economics and Social Sciences”.

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Authors and Affiliations

  1. Istituto di Matematica Finanziaria, Università di Torino, Via Assarotti 3, 10122, Torino, Italy

    Luigi Montrucchio

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  1. Luigi Montrucchio
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Editors and Affiliations

  1. Dipartimento di Matematica per le Decisioni Economiche, Finanziarie, Attuariali e Sociali, Università di Firenze, Via Lombroso 6/17, I-50134, Firenze, Italia

    Franco Gori

  2. Dipartimento di Economia Politica, Università di Siena, Piazza San Francesco 1, I-53100, Siena, Italia

    Lucio Geronazzo

  3. Istituto di Matematica e Statistica, Università di Ancona, Via Pizzecolli 37, I-60121, Ancona, Italia

    Marcello Galeotti

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© 1993 Springer-Verlag Berlin Heidelberg

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Montrucchio, L. (1993). Complexity of Optimal Paths in Strongly Concave Problems. In: Gori, F., Geronazzo, L., Galeotti, M. (eds) Nonlinear Dynamics in Economics and Social Sciences. Lecture Notes in Economics and Mathematical Systems, vol 399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58031-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-58031-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56704-2

  • Online ISBN: 978-3-642-58031-4

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