# Local infimum in optimal control

## TL;DR

This paper introduces the concept of a local infimum in optimal control, extending existing definitions, and establishes existence and necessary conditions that strengthen classical maximum principles.

## Contribution

It defines a new concept of local infimum in optimal control and derives strengthened necessary conditions akin to maximum principles.

## Key findings

- Existence theorem for local infimum
- Necessary conditions resembling maximum principles
- Examples demonstrating the strength of the new conditions

## Abstract

The concept of a local infimum for an optimal control problem is introduced. This definition extends that of an optimal process. For a~local infimum we prove an existence theorem and derive necessary conditions that resemble some family of "maximum principles". Examples are given to demostrate the meaningfulness of the necessary conditions obtained in the present paper, which extend and strengthen the classical results in this field.