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"Unconstrained optimization" as a book category covers the theory, algorithms, and applications of finding minima or maxima of objective functions over unconstrained domains (typically R^n) — that is, problems without explicit equality or inequality constraints. Volumes in this category range from rigorous mathematical treatments of existence, optimality conditions, and convergence/complexity analysis for smooth and nonsmooth, convex and nonconvex problems to practical algorithmic guides on gradient methods, Newton and quasi-Newton methods, line-search and trust-region strategies, coordinate and stochastic approaches, and modern large-scale techniques used in machine learning. These books target mathematicians, engineers, data scientists, and students who need foundations and implementations for iterative solvers, numerical stability, and performance tuning, often including worked examples, software pointers, and application case studies in areas such as signal processing, control, design optimization, and statistical learning.

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