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\title{Necessary Conditions in Dynamic Optimization}
\author{Richard Vinter}
\institute{Imperial College of London}
\email{r.vinter@imperial.ac.uk}

\mymaketitle

\section{Abstract}
Necessary conditions of optimality are a centrepiece of optimal control theory. 
Even in situations in which they do not lead directly to the solution of a particular problem, they have an important role both in 
establishing regularity properties of minimizers and inspiring numerical solution techniques. In this talk, we cover the evolution of this 
field following on from the discovery of the Maximum Principle 50 years ago, recent developments and current open questions. 
Special emphasis is given to an approaches according to which dynamic optimization problems  are formulated as generalized problems in 
the calculus of variations with one independent variable and then far reaching extensions of classical necessary conditions are derived by means 
of non-smooth analysis.
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