Optimization: 100 Examples

When Standard Optimization Methods Meet Their Limits

This book examines optimization problems where familiar methods run into trouble. Rather than a general introduction, it is built around 100 examples that reveal where assumptions fail, solutions behave unexpectedly, or optimality conditions need closer scrutiny. Simon Serovajsky, professor of mathematics at Al-Farabi Kazakh National University, uses these cases to sharpen understanding of optimization and optimal control theory.

What the Examples Reveal

Each example is chosen to illustrate a distinct effect, so the collection avoids repeating the same lesson in different notation. Readers encounter non-uniqueness, absence of minima, failure of classical conditions, singular controls, and other complications that arise in both finite-dimensional minimization and optimal control. The result is a practical diagnostic resource: it helps identify why a method struggles and what alternatives or refinements may be needed.

From One-Variable Minimization to Optimal Control

The opening parts focus on minimization of functions of one variable, including Fermat’s theorem, variational inequalities, and parameter dependence. Later parts move into optimal control problems for systems with a free finite state, covering the maximum principle, alternative methods, uniqueness and sufficiency, and singular controls. Lectures are paired with appendices that extend the central ideas, making the book suitable for both guided study and reference.

Who Will Find It Useful

• Mathematicians working in optimization, control theory, and applied analysis
• Engineers who need to diagnose difficult optimal control problems
• Researchers and graduate students looking for a wide-ranging source of counterexamples and edge cases
• Readers already familiar with standard optimization methods who want to understand their limitations

Why This Collection Stands Out

The examples differ in their properties, so each one has a specific purpose. That variety makes the book more than a problem set; it is a structured investigation of why optimization methods succeed, fail, or require modification. The presentation is accessible while remaining rigorous, and the focus on difficult scenarios makes it a useful companion for theoretical study and practical problem-solving.

Start Exploring Optimization Through Examples

If you want to understand optimization not only as a collection of algorithms but as a field shaped by subtle cases and limitations, this CRC Press title offers a thorough and example-driven route. Digital Delights makes it available as a digital ebook for readers who prefer immediate access to a research reference they can consult again and again.