مقایسهٔ روش‌ها

	بهینه‌سازی دو سطحی (رهبر-پیرو)	برنامه‌ریزی غیرخطی
حوزه	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1998	2006
پدیدآور	Jonathan Bard	Jorge Nocedal & Stephen Wright
نوع	Hierarchical mathematical programming	Continuous mathematical optimization
منبع بنیادین	Bard, J. F. (1998). Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers. ISBN: 978-0-7923-5458-7	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1
نام‌های دیگر	Stackelberg Optimization, Hierarchical Programming, Nested Optimization, İki Düzeyli Optimizasyon	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
مرتبط	3	3
خلاصه	Bilevel optimization is a class of mathematical programming problems in which one optimization problem is nested inside another. The upper-level (leader) problem optimizes its objective subject to constraints that include the solution of a lower-level (follower) problem. Formalized comprehensively by Jonathan Bard in 1998, the framework models hierarchical decision-making where the leader anticipates and accounts for the rational response of the follower.	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.