In layman’s terms, the mathematical science of Optimization is a study of how to make good choices when confronted with conflicting requirements and demands. Optimization is a relatively new wisdom, historically, that can represent balance of real things. The qualifier convex means: when an optimal solution is found, then it is guaranteed to be a best solution; there is no better choice. 

Any convex optimization problem has geometric interpretation. If a given optimization problem can be transformed to a convex equivalent, then this interpretive benefit is acquired. That is a powerful attraction: the ability to visualize geometry of an optimization problem. Conversely, recent advances in geometry and in graph theory hold convex optimization within their proofs’ core. [439] [340] 

This book is about convex optimization, convex geometry (with particular attention to distance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convexity. A virtual flood of new applications follows by epiphany that many problems, presumed nonconvex, can be so transformed: [11] [12] [35, ? 4.3, p.316-322] [61] [97] [163] [166] [294] [318] [326] [385] [386] [436] [439] e.g, sigma delta analog-to-digital (A/D) audio converter antialiasing (Figure 1).