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Nonsmooth analysis provides insights into the local properties of functions that are not differentiable in the classical sense and of sets that are not smooth. Dynamic optimization is a unified framework for studying strategies to control a dynamical system, which optimize a criterion of best performance. Dynamic Optimization brings together many of the important advances in the field, with emphasis on necessary conditions, minimizer regularity and global optimality conditions related to the Hamilton Jacobi equation. 

Features and Topics
An extended overview giving readers easy access to key concepts, while conveying an understanding of the shortcomings of the elementary theory and of how a deeper analysis aims to overcome them. A self-contained exposition of non-smooth analysis emphasizing aspects relevant to optimization. A thorough treatment of necessary conditions of optimality. A comprehensive coverage of dynamic programming.

Prerequisites

Fundamental knowledge of calculus, mathematical analysis, and ordinary differential equations – STEM area.

The course modules will be released progressively according to the schedule below:

• 30th May: Module 1 and Module 2
• 4th June: Module 3 and Module 4
• 12th June: Module 5 and Module 6

The main purpose of these lectures is to provide an extended overview giving easy access to key concepts, results and tools for the study of dynamic optimization problems, with a strong emphasis on those obtained by nonsmooth analytical techniques. Necessary conditions of optimality, the value function and solutions to the Hamilton Jacobi equation in dynamic programming, receive special attention.

The target audience comprises undergraduates, postgraduates, researchers and professionals in systems science, control engineering, optimization and applied mathematics.