An Indirect Sufficiency Proof for the Problem of Lagrange with Differential Inequalities as Added Side Conditions

Louis L. Pennisi

A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 271-292 from Springer

Abstract: Abstract The problem to be considered here consists in finding in a class of arcs $$ C:\rm {y}^{i}(x)(i=1,\cdots ,n;x^{1}\leqq \; x \; \leqq x^{2})$$ joining two fixed points and satisfying a set of differential inequalities and equations of the form $$ \begin{array}{clclclcl}{\phi^{\beta}(x,y,\dot{y}\geqq 0),} & {{\Psi}^{p}(x,y,\dot{y})= 0}\end{array} $$ that one which minimizes the integral $$ I(c)={\int^{x^{2}}_{x^{1}}} \; f(x,y,\dot{y})dx. $$

Date: 2014
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DOI: 10.1007/978-3-0348-0439-4_13

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