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Nonlinear optimization as a book category covers the theory, algorithms, and applications for finding minima or maxima of functions when the relationship between variables is not linear; it includes both unconstrained and constrained problems, convex and nonconvex formulations, and distinctions between local and global solutions. Books in this genre range from rigorous mathematical texts on existence, optimality conditions (KKT, Lagrange multipliers), and convergence theory, to algorithmic and computational treatments of gradient, Newton and quasi-Newton methods, interior-point and sequential quadratic programming, derivative-free and global-search strategies, and practical implementation issues and software. They often assume background in multivariable calculus, linear algebra, and numerical analysis, and are aimed at graduate students, researchers, and practitioners in fields like engineering, operations research, data science, and machine learning. Applied volumes emphasize modeling, case studies, and code for real-world problems (parameter fitting, control, design optimization), while advanced monographs delve into complexity, stochastic and nonsmooth optimization, and modern research topics.

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