Linganisha mbinu

	Utekelezaji wa Namba Kamili	Upangaji wa Hisabati Usio na Mstari
Nyanja	Uboreshaji	Uboreshaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1958	2006
Mwanzilishi	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Jorge Nocedal & Stephen Wright
Aina	Mathematical optimisation — exact combinatorial method	Continuous mathematical optimization
Chanzo asilia	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
Majina mbadala	IP, MIP, mixed-integer programming, mixed-integer linear programming	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
Zinazohusiana	4	3
Muhtasari	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.