linear programming
Also known as LP, linear optimization
programming method to achieve the best outcome in a mathematical model
AI overview
Linear programming is a mathematical method for finding the best possible solution to a problem where you need to optimize something (like maximizing profit or minimizing cost) while staying within certain constraints or limits. It matters because it helps businesses and organizations make efficient decisions about how to allocate their resources in real-world situations like production planning, scheduling, and resource management.
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Research
5,796 papers- Design of complex neuroscience experiments using mixed-integer linear programming.ReviewNeuron · 2021Slivkoff S, Gallant JLDOI: 10.1016/j.neuron.2021.02.019
- Linear Programming from Fibonacci to Farkas.Annals of science · 2021Biggs NDOI: 10.1080/00033790.2020.1811377
- Linear programming: a mathematical tool for analyzing and optimizing children's diets during the complementary feeding period.ReviewJournal of pediatric gastroenterology and nutrition · 2003Briend A, Darmon N, Ferguson E et al.DOI: 10.1097/00005176-200301000-00006
- Linear programming based computational technique for leukemia classification using gene expression profile.PloS one · 2023Ilyas M, Aamir KM, Manzoor S et al.DOI: 10.1371/journal.pone.0292172
Article
A pictorial representation of a simple linear program with two variables and six inequalities. The set of feasible solutions is depicted in yellow and forms a polygon, a 2-dimensional polytope. The optimum of the linear cost function is where the red line intersects the polygon. The red line is a level set of the cost function, and the arrow indicates the direction in which we are optimizing. A closed feasible region of a problem with three variables is a convex polyhedron. The surfaces giving a fixed value of the objective function are planes (not shown). The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).