Hello Jared, you will have to keep the u[i] variables as columns in your problem. And the objective will only have nonzereo coefficients w[i] for these columns.
Have a look at http://www.xypron.de/projects/linopt/examples.html to see how accessing the GLPK API can be eased by a wrapper. Best regards Xypron -------- Original-Nachricht -------- > Datum: Tue, 4 Sep 2012 17:39:54 -0700 > Von: Jared Miller <jarednmil...@gmail.com> > An: GLPK help <help-glpk@gnu.org> > Betreff: Re: [Help-glpk] C API: Setting up a least-absolute-deviation > Robbie, > > Thanks for the reply. To clarify, I'm not asking for help with the basics > of the C API (it looks pretty straightforward if your problem is in the > right form); rather I'm asking how to translate my high-level formulation > (which includes the dummy u[i]'s) into the low-level formulation (with only > auxiliary and structural variables, objective only in terms of the structural, > and all the bounds constant). > > I'll try loading/translating my MathProg file into a "glp_prob" struct and > examining the internal translation. Eventually I need to work on > abstracting a way of getting problems of this type into the GLPK low-level > form. > > On Sep 1, 2012, at 11:25 AM, Robbie Morrison wrote: > > > > > Hello Jared > > > > ------------------------------------------------------------ > > To: help-glpk@gnu.org > > Subject: [Help-glpk] C API: Setting up a least-absolute-deviation > > Message-ID: <2f1bd370-dd45-45b3-af7e-6d41d9ccb...@gmail.com> > > From: Jared Miller <jarednmil...@gmail.com> > > Date: Fri, 31 Aug 2012 15:52:11 -0700 > > ------------------------------------------------------------ > > > >> I have an absolute value objective function, minimizing > >> the sum of abs( s[i] - x[i] ) for two vectors s and x, > >> with the constraints given by Ax = b where A is a large > >> but very sparse matrix. > >> > >> So I'm using a dummy vector "u" in a MathProg model: > >> > >> minimize least_abs_dev: sum {i in I} (u[i]); > >> s.t. constr1{i in I} : b[i] = sum{j in I} (A[i,j] * x[j]); > >> s.t. constr2{i in I} : u[i] >= (s[i] - x[i]); > >> s.t. constr3{i in I} : u[i] >= -(s[i] - x[i]); > >> > >> I also eventually want to incorporate weights into the > >> objective: > >> > >> minimize least_abs_dev: sum {i in I} (u[i] * w[i]); > >> > >> I've got this type of model working using MathProg > >> and glpsol, but now I'm trying to figure out how to > >> translate it to the strict form required by the C > >> API. Has anyone done this? What's the best way to > >> go about it? I'm going to need high performance on > >> some large problems. > >> > >> I am fairly new to optimization and GLPK. Any help > >> would be much appreciated. > >> > >> - JM > > > > I'm not exactly sure what your question is, but here > > are some observations base on my experiences. I'm > > going to assume C++ too. > > > > First, there are some GLPK wikibook pages: > > > > http://en.wikibooks.org/wiki/GLPK/Using_the_GLPK_callable_library > > http://en.wikibooks.org/wiki/GLPK >> sections 14.1 thru 14.6 > > > > Second, you will probably need to understand how the > > GLPK MathProg translator translates your high-level > > model into a low-level problem -- unless you have some > > other insights based on the theoretical formulation of > > your problem. One way of doing this is to formulate > > simple instances of your model and examine the problem > > in say CPLEX LP format. > > > > http://en.wikibooks.org/wiki/GLPK/Interoperability#CPLEX.C2.A0LP_format > > > > I ended up writing a C++ class that interrogated the > > GLPK problem object and produces an HTML table to view > > in a web browser. Detailed routine work which > > invariably took several loops to get right. > > > > Third, some kind of abstraction between your model > > formulation and the raw GLPK calls could be useful. > > One relatively simple example can be found here: > > > > http://en.wikibooks.org/wiki/GLPK/IAJAAR.H_project > > > > I wrote a large class to provide a semi-intelligent > > interface with GLPK. This class tracked rows and > > columns as they were added and performed integrity > > checks too. Then I had another abstraction above this > > related to my domain modeling needs. A background in > > computer science can help here. > > > > In any event, I am guessing that you will need to know > > exactly how your structural matrix and your objective > > vector are being build, one API call at a time. > > > > REFERENCES > > > > One reference. Not sure exactly how useful it is. > > I could dig out some more if you can give me a better > > idea of where exactly you are headed. > > > > @incollection{ > > Author = {Hultberg, Tim H.}, > > Title = {Formulation of linear optimization problems in C++ [includes > > MIP]}, > > BookTitle = {Programming languages and systems in computational > > economics and finance}, > > Editor = {Nielsen, Soren S.}, > > Publisher = {Kluwer Academic Publishers}, > > Address = {Boston, MA, USA}, > > Pages = {199-229}, > > Note = {Chapter 6}, > > Year = {2002} } > > > > HTH, Robbie > > --- > > Robbie Morrison > > PhD student -- policy-oriented energy system simulation > > Technical University of Berlin (TU-Berlin), Germany > > University email (redirected) : morri...@iet.tu-berlin.de > > Webmail (preferred) : rob...@actrix.co.nz > > [from Webmail client] > > > > > > > _______________________________________________ > Help-glpk mailing list > Help-glpk@gnu.org > https://lists.gnu.org/mailman/listinfo/help-glpk _______________________________________________ Help-glpk mailing list Help-glpk@gnu.org https://lists.gnu.org/mailman/listinfo/help-glpk
