Порівняння методів

	Цілочисельне програмування	Нелінійне програмування
Галузь	Оптимізація	Оптимізація
Родина	Process / pipeline	Process / pipeline
Рік появи	1958	2006
Автор методу	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Jorge Nocedal & Stephen Wright
Тип	Mathematical optimisation — exact combinatorial method	Continuous mathematical optimization
Основоположне джерело	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
Інші назви	IP, MIP, mixed-integer programming, mixed-integer linear programming	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
Пов'язані	4	3
Підсумок	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.