
quadprog2  convex QP solver 1.0 File ID: 79229 


 quadprog2  convex QP solver 1.0 License: Freeware File Size: 30.7 KB Downloads: 17
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quadprog2  convex QP solver 1.0 Description 

Description: QUADPROG2  Convex Quadratic Programming Solver Featuring the SOLVOPT freeware optimizer
New for version 1.1: * Significant speed improvement * Geometric Preconditioning * Improved Error Checking
USAGE: [x,v] = quadprog2(H,f,A,b) [x,v] = quadprog2(H,f,A,b,guess) [x,v,opt] = ...
Minimizes the function v = 0.5*x'*H*x + f*x subject to the constraint A*x <= b. Initial guess is optional.
("opt" returns SOLVOPT data for advanced use. Details are available in the SOLVOPT documentation at the website identified below.)
Notes: (1) For a problem with 100 variables and 300 constraints, you will often get a result in under 5 seconds. However, sometimes the optimizer has to work longer (see below) for difficult optimizations. Alerts are provided. (Note: The calculation time is more sensitive to the number of variables than it is to the number of contraints.) (2) Geometric preconditioning is undertaken for 10 or more dimensions to greatly reduce calculation time. (With fewer than 10 dimensions, there is negligible benefit, so the preconditioning calculations are omitted.) (3) Geometric preconditioning can impair the convergence of some difficult optimizations. When this occurs, the optimization is attempted again without the preconditioning. (4) x and guess are column vectors. f is a row vector. They will be converted if necessary. (5) This mfile incorporates the SOLVOPT version 1.1 freeware optimizer, which has been wholly reproduced, except for a few slight modifications for convenience in parameter passing. (6) SolvOpt is a general nonlinear local optimizer, written by Alexei Kuntsevich & Franz Kappel, and is available (as of this writing) as freeware from: http://www.unigraz.at/imawww/kuntsevich/solvopt/ (7) This Matlab function requires a convex QP problem with a positivedefinite symmetric matrix H. This is a somewhat trivial application of a general solver like SOLVOPT, but the use of precomputed gradient vectors herein makes the solution fast enough to warrant use. (8) Any local solution of a convex QP is also a global solution. Hence, your results will be globally optimal. (9) Relative precision in the objective function is set to 1e6. (10) Absolute precision in constraint violation is 1e6 or better. (11) This program does not require the Optimization Toolbox (12) ver 1.0: intial writing, Michael Kleder, June 2005 (13) ver 1.1: geometric preconditioning, Michael Kleder, July 2005
EXAMPLE: % Convex QP with 100 variables and 300 constraints: n = 100; c = 300; H = rand(n); H=H*H'; f=rand(1,n); A=rand(c,n)*21; b=ones(c,1); tic x = quadprog2(H,f,A,b) toc
License: Freeware Related: alexei, kuntsevich, franz, optimizerwritten, Local, solvopt, General, nonlinear, kappel, andis, convex, problemwith, positivedefinite, requires, matlab, Writing, fromhttpwwwunigrazatimawwwkuntsevichsolvopt, passing, Parameter, converted O/S:BSD, Linux, Solaris, Mac OS X File Size: 30.7 KB Downloads: 17


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