قارن الطرق

	التحسين ثنائي المستوى (القائد-التابع)	البرمجة الصحيحة	البرمجة غير الخطية
المجال	التحسين	التحسين	التحسين
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1998	1958	2006
صاحب الطريقة	Jonathan Bard	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Jorge Nocedal & Stephen Wright
النوع	Hierarchical mathematical programming	Mathematical optimisation — exact combinatorial method	Continuous mathematical optimization
المصدر التأسيسي	Bard, J. F. (1998). Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers. ISBN: 978-0-7923-5458-7	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1
الأسماء البديلة	Stackelberg Optimization, Hierarchical Programming, Nested Optimization, İki Düzeyli Optimizasyon	IP, MIP, mixed-integer programming, mixed-integer linear programming	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
ذات صلة	3	4	3
الملخص	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.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.	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.