Hi all, The problem I am trying to solve is the following: I have a 'trace' of half-hourly data across an entire year - i.e. I have 17,500 observations (one for every half-hour of every day of a year). The data follows a daily, weekly and seasonal pattern that is important to preserve. What I want to do is scale this 'trace' of data in a way that minimizes distortion to the 'shape' of the original observations while achieving two things: (i) I want the new mean of this set of observations to be a certain value (lets say 5% higher than my initial set) and I want the new maximum point of this set to be a certain value (lets say 10% higher than my initial set).
I have approached this problem as a constrained-optimization problem: to minimize the sum of squared deviations subject to the mean and max of the new set of observations achieving certain values. I have created a simple proof of concept in excel using Solver, and this approach appears to work. My objective function to be minimized is: sum((xi-1)^2), where each xi is a unique scaling factor for each half-hourly observation and where these xi's represent the decision variables of the constrained-optimization problem. Put differently, the problem is to select each xi such that (i) you minimize the sum of squared deviations from 0 (xi = 1 for all xi results in the original data set and hence no deviation) while (ii) achieving a new mean and max... Having researched constrained optimization in R and having read the "CRAN Task View: Optimization and Mathematical Programming" document (http://cran.r-project.org/web/views/Optimization.html), I have been experimenting with lsei() from the limSolve package. I have worked through the simple examples in the limSolve user manual, but am struggling to correctly set up and solve my problem. My questions to anyone experienced in solving such problems and/or with using lsei are the following: - Do you think lsei() is the best function to use to solve this problem? I need to be able to set equality constraints and the problem is non-linear, which appears to rule out most other options (optim() for example) Assuming lsei() is appropriate: - The lsei() documentation states that matrix 'A' is a "a numeric matrix containing the coefficients of the quadratic function to be minimised, (Ax - b)^2..." and that vector 'B' is a "numeric vector containing the right-hand side of the quadratic function to be minimized". - Assume that y = sum((Ax - b)^2) is the quadratic function to be minimized. - Are the "coefficients of the quadratic function to be minimized" 'A' and 'b' respectively? If so, how are they entered in matrix 'A'? I.e. is column 1 of 'A' = all the A's, column 2 of 'A' = all the B's and each row of 'A' a new argument of sum()? (In my case, a new data point?) - Alternatively, are the "coefficients of the quadratic to be minimized" the coefficients after expanding y = (Ax - b)^2)? In which case you would have: y = (A^2)*(x^2) -2Ab*x + b^2. Defining '(A^2)' as 'd', '2Ab' as 'e' and 'b^2' as 'f' would then give you y = d(x^2) -ex + f, with the coefficients being 'd', 'e' and 'f' respectively. If this is the case, again how are they entered into matrix 'A' and in what order? My apologies for the verbose posting - I have attempted to be as concise as possible. R version: 2.9.2 OS: Windows 7, 64-bit limSolve version: 1.5.1 Regards, Liam ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
