{"id":1379,"date":"2023-06-01T08:30:20","date_gmt":"2023-06-01T08:30:20","guid":{"rendered":"https:\/\/nag.com\/?page_id=1379"},"modified":"2024-12-16T13:36:04","modified_gmt":"2024-12-16T13:36:04","slug":"mixed-integer-nonlinear-programming-minlp","status":"publish","type":"page","link":"https:\/\/nag.com\/mixed-integer-nonlinear-programming-minlp\/","title":{"rendered":"Mixed Integer Nonlinear Programming (MINLP)"},"content":{"rendered":"\n
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Mixed Integer Nonlinear Programming (MINLP)<\/h1>\n \n
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Mixed\u00a0integer programming problems are defined as those where some or all of the decision variables are only allowed to be integers. This is typically required in a range of real world applications in allocation and planning problems where the discrete variables represent quantities, such as the number of individual shares to be held, or the number of pipelines need, or the number of oil-spill cleaning locations to be deployed, and require integer values for the solution.<\/p>\n

Many applications lead to mathematical models which can be written as Mixed Integer Linear Programming (MILP) or as Mixed-Integer Quadratic Programming (MIQP) problems \u2013 that is problems with linear constraints and with linear or with quadratic objective functions. However, for some this might not be enough to capture the key characteristics of a real problem. In these cases fully nonlinear models are needed \u2013 so a solver has to handle the combinatorial difficulty of optimizing over discrete variable sets together with the issues of handling nonlinear functions.<\/p>\n

Such models, where a MINLP solver is useful, arise in scientific, engineering, and financial applications. Examples can be found in many areas including:<\/p>\n