30 research outputs found
Nonessential functionals in multiobjective optimal control problems
We address the problem of obtaining well-defined criteria for multiple criteria optimal control problems. Necessary and sufficient conditions for an objective functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in multiobjective optimal control problems
Fractional calculus of variations in terms of a generalized fractional integral with applications to physics
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed. Copyright 2012 Tatiana Odzijewicz et al
A General Backwards Calculus of Variations via Duality
We prove Euler-Lagrange and natural boundary necessary optimality conditions
for problems of the calculus of variations which are given by a composition of
nabla integrals on an arbitrary time scale. As an application, we get
optimality conditions for the product and the quotient of nabla variational
functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010;
accepted for publication 08-July-201
Backward variational approach on time scales with an action depending on the free endpoints
We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator. © 2011 Verlag der Zeitschrift für Naturforschung, Tübingen
Lie group classifications and exact solutions for time-fractional Burgers equation
Lie group method provides an efficient tool to solve nonlinear partial
differential equations. This paper suggests a fractional Lie group method for
fractional partial differential equations. A time-fractional Burgers equation
is used as an example to illustrate the effectiveness of the Lie group method
and some classes of exact solutions are obtained.Comment: 9 pp, accepte
Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales
We obtain Euler-Lagrange and transversality optimality conditions for
higher-order infinite horizon variational problems on a time scale. The new
necessary optimality conditions improve the classical results both in the
continuous and discrete settings: our results seem new and interesting even in
the particular cases when the time scale is the set of real numbers or the set
of integers.Comment: This is a preprint of a paper whose final and definite form will
appear in Journal of Optimization Theory and Applications (JOTA). Paper
submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for
publication 15-April-201
Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
We consider problems of the calculus of variations on unbounded time scales.
We prove the validity of the Euler-Lagrange equation on time scales for
infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for
publication in "Optimization Letters"
Higher-order variational problems of Herglotz type
We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given
On the diamond-alpha riemann integral and mean value theorems on time scales
We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat's theorem for stationary points is also proved, as well as Rolle's, Lagrange's, and Cauchy's mean value theorems on time scales. ©Dynamic Publishers, Inc