Σύγκριση μεθόδων

	Κυρτή Βελτιστοποίηση	Μη Γραμμικός Προγραμματισμός	Στιβαρή Βελτιστοποίηση
Πεδίο	Βελτιστοποίηση	Βελτιστοποίηση	Βελτιστοποίηση
Οικογένεια	Process / pipeline	Process / pipeline	Process / pipeline
Έτος προέλευσης	2004	2006	1970s theoretical roots; modern tractable form from late 1990s–2004
Δημιουργός	Stephen Boyd & Lieven Vandenberghe	Jorge Nocedal & Stephen Wright	Ben-Tal, El Ghaoui & Nemirovski (seminal book, 2009); Bertsimas & Sim (tractable polyhedral formulation, 2004)
Τύπος	Mathematical optimization framework	Continuous mathematical optimization	Mathematical programming framework
Θεμελιώδης πηγή	Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press. ISBN: 978-0-521-83378-3	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1	Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009). Robust Optimization. Princeton University Press. ISBN: 9780691143682
Εναλλακτικές ονομασίες	Convex Programming, Disciplined Convex Programming, Dışbükey Optimizasyon, Convex Mathematical Programming	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama	minimax optimization, worst-case optimization, Gürbüz Optimizasyon (Robust Optimization)
Συναφείς	3	3	5
Σύνοψη	Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Formalized and popularized by Stephen Boyd and Lieven Vandenberghe in their landmark 2004 textbook, the framework unifies a wide family of problems — including linear programming, quadratic programming, semidefinite programming, and second-order cone programming — under a single theoretical roof. Its defining property is that any locally optimal solution is also globally optimal, making it tractable and reliable for engineering, statistics, machine learning, and operations research.	Nonlinear programming (NLP) is a branch of mathematical optimization concerned with problems in which the objective function or at least one constraint is nonlinear. Formalized comprehensively by Jorge Nocedal and Stephen Wright in their seminal 2006 text, NLP encompasses gradient-based algorithms — including sequential quadratic programming (SQP), interior-point methods, and quasi-Newton approaches — for finding locally or globally optimal solutions to continuous decision problems arising across engineering, economics, and the physical sciences.	Robust optimization is a mathematical programming framework, formalised by Ben-Tal and Nemirovski in the late 1990s and made broadly tractable by Bertsimas and Sim (2004), that finds decisions guaranteed to perform acceptably under every scenario within a predefined uncertainty set — rather than assuming parameter values are known exactly. Instead of optimising for a single expected outcome, it minimises the worst-case objective across all plausible realisations of uncertain data.