방법 비교
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| 정수 계획법(IP) 및 혼합 정수 계획법(MIP)× | 비선형 계획법× | |
|---|---|---|
| 분야 | 최적화 | 최적화 |
| 계열 | Process / pipeline | Process / pipeline |
| 기원 연도≠ | 1958 | 2006 |
| 창시자≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Jorge Nocedal & Stephen Wright |
| 유형≠ | Mathematical optimisation — exact combinatorial method | Continuous mathematical optimization |
| 원전≠ | 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 |
| 별칭≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama |
| 관련≠ | 4 | 3 |
| 요약≠ | 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. |
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