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## Linear Programming with Nonlinear Programming Solvers

version 1.0 (20.1 KB) by John Hedengren

### John Hedengren (view profile)

Similar interface to linprog but solution with nonlinear programming solvers such as IPOPT

Updated 09 Feb 2015

apm_linprog Linear programming.
y = apm_linprog(f,A,b,Aeq,beq,LB,UB,X0) writes a linear programming model in APMonitor Modeling Language and attempts to solve the linear programming problem:
min f'*x subject to: A*x <= b, Aeq*x = beq
x

lb and ub are a set of lower and upper bounds on the design variables, x, so that the solution is in the range lb <= x <= ub. Use empty matrices for any of the arguments. Set lb(i) = -1e20 if x(i) has no lower limit and set ub(i) = 1e20 if x(i) has no upper limit. x0 is the initial guess and starting point to x. This is similar to the Matlab linprog solver but uses different solvers such as IPOPT, APOPT, and BPOPT to solve the LP. Additional nonlinear constraints can be added to the lp.apm model for nonlinear programming solution with support for possible mixed-integer variables.

The solution is returned in the structure y with y.names (variable names), y.values (variable values), y.nvar (number of variables), and y.x (a structure containing each variable and value).

Example usage is below:

clear all; close all; clc

% example Linear program
f = [-5; -4; -6];
A = [1 -1 1
3 2 4
3 2 0];
b = [20; 42; 30];
Aeq = [];
beq = [];
lb = zeros(3,1);
ub = [];
x0 = [];

% generate and solve APMonitor LP model
y1 = apm_linprog(f,A,b,Aeq,beq,lb,ub,x0);

% compare solution to linprog (MATLAB)
y2 = linprog(f,A,b,Aeq,beq,lb,ub,x0);

disp('Validate Results with MATLAB linprog')
for i = 1:max(size(f)),
disp(['x[' int2str(i) ']: ' num2str(y1.values(i)) ' = ' num2str(y2(i))])
end

John Hedengren

### John Hedengren (view profile)

The server is available for download from http://apmonitor.com/wiki/index.php/Main/APMonitorServer (Windows) or http://apmonitor.com/wiki/index.php/Main/APMonitorServerLinux (Linux). By default, this program uses a public web-server as others have commented. However, users can also download and use a local server (no Internet connection required).

##### MATLAB Release Compatibility
Created with R2014b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux