Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

Necessary Condition for Path Partitioning Constraints

Given a directed graph G, the K node-disjoint paths problem consists in finding a partition of G into K node-disjoint paths, such that each path ends up in a given subset of nodes in G. This article provides a necessary condition for the K node-disjoint paths problem which combines (1) the structure of the reduced graph associated with G, (2) the structure of each strongly connected component o...

Second-order optimality conditions for a Bolza problem with mixed constraints ?

For an optimal control problem with fixed initial state and constraints on admissible controls we propose new second-order necessary optimality conditions using second-order tangents to the set of controls. In the absence of constraints on controls, our conditions are stronger than those of Gilbert and Bernstein (1983). Then, we investigate optimal control problems with fixed initial state and ...

Bolza Problems with General Time Constraints

This work provides necessary conditions for optimality in problems of optimal control expressed as instances of the Generalized Problem of Bolza, with the added feature that the fundamental planning interval is allowed to vary. A central product of the analysis is a generalization of the conservation-of-Hamiltonian condition for problems on either fixed or variable intervals. The results allow ...

A Necessary Condition for Weyl-Heisenberg Frames