This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice Rene Frechet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical differential calculus, including the chain rule, making it a natural framework for initiating a large audience of undergraduates and non-mathematicians into the world of nondifferentiable optimization. Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition: builds upon its prior edition's foundations in Hadamard semidifferential calculus, showcasing new material linked to convex analysis and nonsmooth optimization; presents a modern treatment of optimization and Hadamard semidifferential calculus while remaining at a level that is accessible to undergraduate students; and challenges students with exercises related to problems in such fields as engineering, mechanics, medicine, physics, and economics and supplies answers in Appendix B.