قارن الطرق

	البرمجة الصحيحة	البرمجة غير الخطية
المجال	التحسين	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1958	2006
صاحب الطريقة	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Jorge Nocedal & Stephen Wright
النوع	Mathematical optimisation — exact combinatorial method	Continuous mathematical optimization
المصدر التأسيسي	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	IP, MIP, mixed-integer programming, mixed-integer linear programming	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
ذات صلة	4	3
الملخص	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.