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Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers....

Hamiltonian form of the maximum principle

Revaz Gamkrelidze (2009)

Control and Cybernetics

Lehrbuch der Variationsrechnung [Book]

Adolf Kneser (1900)

O 19. a 20. Hilbertově problému

Jiří Souček, Vladimír Souček, Jana Stará (1977)

Pokroky matematiky, fyziky a astronomie

On the development of Pontryagin's Maximum Principle in the works of A. Ya. Dubovitskii and A. A. Milyutin

Andrei Dmitruk (2009)

Control and Cybernetics

Optimal networks for mass transportation problems

Alessio Brancolini, Giuseppe Buttazzo (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In the framework of transport theory, we are interested in the following optimization problem: given the distributions $μ^{+}$ of working people and $μ^{-}$ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of $μ^{+}$ from $μ^{-}$ with respect to a metric which depends on the transportation network....

Optimal networks for mass transportation problems

Alessio Brancolini, Giuseppe Buttazzo (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ+ of working people and µ- of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ+ from µ- with respect to a metric which depends on the transportation...

The maximum Principle of optimal control: A history of ingenious ideas and missed opportunities

Hans Pesch, Michael Plail (2009)

Control and Cybernetics

Variational Principles in the General Theory of Relativity.

H. Rund, D. Lovelock (1972/1973)

Jahresbericht der Deutschen Mathematiker-Vereinigung

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