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Questions tagged [linear-programming]

An optimization technique for minimizing or maximizing a function of several variables in the presence of constraints where all relationships are linear.

Linear Programming is a mathematical optimization technique for minimizing or maximizing a linear function of several variables (called the objective function) subject to several linear constraints. The objective function and the set of constraints are collectively called the Linear Program.

The dual Simplex Method is a commonly used solution technique in Linear Programming. There are several commercial and open-source software packages for solving linear programs.

Brief history:
1939. Production, planning. [Kantorovich]
1947. Simplex algorithm. [Dantzig]
1947. Duality. [von Neumann, Dantzig, Gale-Kuhn-Tucker]
1947. Equilibrium theory. [Koopmans]
1948. Berlin airlift. [Dantzig]
1975. Nobel Prize in Economics. [Kantorovich and Koopmans]
1979. Ellipsoid algorithm. [Khachiyan]
1984. Projective-scaling algorithm. [Karmarkar]
1990. Interior-point methods. [Nesterov-Nemirovskii, Mehorta, ...]

External links:

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What algorithm should I use to find the minimum flow on a digraph where there are lower bounds but not upper bounds on flow?

What algorithm should I use to find the minimum flow on a digraph where there are lower bounds, but not upper bounds on flow? Such as this simple example: In the literature this is a minimum cost flow problem. In my case however the cost is the…
jwezorek
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Linear programming library for .NET / C#

I need to solve an under-determined linear system of equations and constraints, then find the particular solution that minimises a cost function. This needs to be done in purely portable managed code that will run in .NET and Mono. What freely…
Dylan
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How to make cplex not output to terminal

I am using the IBM cplex optimizer to solve an optimization problem and I don't want all terminal prints that the optimizer does. Is there a member that turns this off in the IloCplex or IloModel class? These are the prints about cuts and…
DiegoNolan
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Why solving Knapsack problem is not considered as linear programming?

Why isn't the knapsack problem included under the category of linear programming algorithms in spite of the fact that the Knapsack problem statement seems similar to the problems in linear programming?
user1543957
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Is there an Integer Linear Programming software that returns also non-optimal solutions?

I have an integer linear optimisation problem and I'm interested in feasible, good solutions. As far as I know, for example the Gnu Linear Programming Kit only returns the optimal solution (given it exists). This takes endless time and is not…
Turion
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How to visualize feasible region for linear programming (with arbitrary inequalities) in Numpy/MatplotLib?

I need to implement a solver for linear programming problems. All of the restrictions are <= ones such as 5x + 10y <= 10 There can be an arbitrary amount of these restrictions. Also , x>=0 y>=0 implicitly. I need to find the optimal solutions(max)…
Arturo
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Maximize consumption Energy

There are three types of foods were provided i.e. meat, cake and pizza and N different stores selling it where, i can only pick one type of food from each store. Also I can only buy items in A, B and C numbers where 'A' means, Meat from total 'A'…
Ndp
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Hungarian algorithm: multiple jobs per worker

Is there an extension of the Hungarian algorithm that caters for the assignment of multiple jobs per worker? In its simplest form, the algorithm assigns a single job to a single worker. My application is a profit maximization problem, with 3…
Richard Ball
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Pyomo can't locate GLPK solver

I'm trying to use the GLPK solver with Pyomo. I have a working model that's been tested, but keep getting an error saying GLPK can't be found. WARNING: Could not locate the 'glpsol' executable, which is required for solver 'glpk' I've installed…
Dylan Cross
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Recommended library for linear programming in .Net?

Can anyone recommend a library - free, or commercial but affordable ( There are some listed here: http://en.wikipedia.org/wiki/Linear_programming#Solvers_and_scripting_.28programming.29_languages ....but I am just starting out with LP and hope…
tbone
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Linear Programming library for iOS

I am looking for an iOS library that enables solving LP, IP, BIP, MIP for an application I am developing. I've found GLPK but have no idea how to compile it for iOS, and after searching the web for some time, I did not find anything interesting...…
Edgepo1nt
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Python server "Aborted (Core dumped)"

I use web.py to create a Python web server. This server is called to solve linear programming problems, and it uses the library CBC to do that. Every once in a while, the server crashes with a log that looks like that: 78.243.184.3:56271 - -…
Arnaud
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PyInstaller .exe file does nothing

After 3 days, I can't get a python program packaged into a .exe file. I've tried py2exe (which continuously missed modules), and PyInstaller. Here's the complicated part. My program uses a lot of additional installed modules (coopr, pyomo,…
Dylan Cross
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Sparse constrained linear least-squares solver

This great SO answer points to a good sparse solver for Ax=b, but I've got constraints on x such that each element in x is >=0 an <=N. Also, A is huge (around 2e6x2e6) but very sparse with <=4 elements per row. Any ideas/recommendations? I'm…
Jacob
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How Can an Elastic SubProblem in PuLP be used as a Constraint?

In Python PuLP, a linear programming constraint can be turned into an elastic subproblem. http://www.coin-or.org/PuLP/pulp.html?highlight=lpsum#elastic-constraints Solving the subproblem optimizes the distance from the target value. Of course, the…
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