This book is a sequel to the 116 Algebraic Inequalities from the AwesomeMath Year-round Program and 118 Inequalities for Mathematics Competitions . It delves into other elementary techniques but also powerful methods and generalizations for constrained optimization in the theory of inequalities. In the first section, the reader will encounter each of Abel's, Newton's, Maclaurin's, and Blundon's inequalities, the method of mathematical induction, the "mixing" and "stronger mixing" variable methods, and the method of Lagrange multipliers. The next sections are dedicated to the proposed problems, which are divided into introductory and advanced. Each problem is given at least one complete solution, and many problems have multiple solutions.