<abstract xmlns="http://www.w3.org/1999/xhtml"><p> This article deals with optimizing problems whose restrictions are nonholonomic. The central issue relates to dual nonholonomic programs (what they mean and how they are solved?) when the nonholonomic constraints are given by Pfaff equations. We emphasize that nonholonomic critical points are not the classical ones and that the nonholonomic Lagrange multipliers are not the classical (holonomic) Lagrange multipliers. Topological significance of Lagrange multipliers and dual function theory introduced by EDO and EDP are key results. Also new Riemannian geometries attached to a given nonholonomic constrained optimization problem are introduced. The original results are surprising and include: (i) aspects derived from the Vranceanu theory of nonholonomic manifolds, and from the geometric distributions theory, (ii) optimal problems in Darboux canonical coordinates. </p></abstract>

This article deals with optimizing problems whose restrictions are nonholonomic. The central issue relates to dual nonholonomic programs (what they mean and how they are solved?) when the nonholonomic constraints are given by Pfaff equations. We emphasize that nonholonomic critical points are not the classical ones and that the nonholonomic Lagrange multipliers are not the classical (holonomic) Lagrange multipliers. Topological significance of Lagrange multipliers and dual function theory introduced by EDO and EDP are key results. Also new Riemannian geometries attached to a given nonholonomic constrained optimization problem are introduced. The original results are surprising and include: (i) aspects derived from the Vranceanu theory of nonholonomic manifolds, and from the geometric distributions theory, (ii) optimal problems in Darboux canonical coordinates.

Dualities in Nonholonomic Optimization

University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Mathematics and Informatics, Splaiul Independentei 313, RO-060042, Bucharest,

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Dualities in Nonholonomic Optimization"}

This article deals with optimizing problems whose restrictions are nonholonomic. The central issue relates to dual nonholonomic programs (what they mean and...

Dualities in Nonholonomic Optimization

Published Online: Dec 30, 2016

Page range: 149 - 166

Received: Oct 27, 2016

Accepted: Dec 12, 2016

DOI: https://doi.org/10.1515/awutm-2016-0020

Keywords
optimization, Pfaff nonholonomic constraints, dual nonholonomic programs

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Dualities in Nonholonomic Optimization

Published Online: Dec 30, 2016

Page range: 149 - 166

Received: Oct 27, 2016

Accepted: Dec 12, 2016

DOI: https://doi.org/10.1515/awutm-2016-0020

Keywordsoptimization, Pfaff nonholonomic constraints, dual nonholonomic programs

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
optimization, Pfaff nonholonomic constraints, dual nonholonomic programs