forum.alglib.nethttp://forum.alglib.net/ getting started with Linear (or Quadratic) Programminghttp://forum.alglib.net/viewtopic.php?f=2&t=4439 Page 1 of 1

 Author: gene [ Wed Apr 13, 2022 3:59 pm ] Post subject: getting started with Linear (or Quadratic) Programming Please point me to relevant examples and/or APIs in ALGLIB.I want to find the vector x whose objective functionminimizes th L1 distance of x from a constant vector x0where L1 distance = sum of absolute values = sum abs((x(i)-x0(i))and subject to this set of linear constraints:x(i+1) - x(i) >= constant(i) for i = 1..n-1 (i.e. x values in ascending order, with specified minimum spacing)x(1) >= min_constantx(n) <= max_constantIf I can get this working, then I want to try alternative distance metricsL2 distance = sum of squared differences = sum (x(i)-x0(i)**2L-infinity distance = max of absolute values = max abs((x(i)-x0(i))Eventually, I want to extend the problem to two dimensions, with each x a point in the x-y plane.

 Author: gene [ Thu Apr 14, 2022 11:54 pm ] Post subject: Re: getting started with Linear (or Quadratic) Programming I studied the manual and think I found the right examples:For the L1 distance objective function which is discontinuous I will try:Nonsmooth nonlinearly constrained optimizationhttps://www.alglib.net/translator/man/manual.cpython.html#example_minns_d_nlcFor the L2 distance objective function which is quadratic I will try:Linearly constrained dense quadratic programminghttps://www.alglib.net/translator/man/manual.cpython.html#example_minqp_d_lc1

 Author: tonyturtletwn [ Fri Jul 15, 2022 3:20 pm ] Post subject: Re: getting started with Linear (or Quadratic) Programming I think L1 norm minimization can be cast as a linear programming problem.Create non-negative dummy variables e_0l, e_0r, e_1l, e_1r, ...then set equality constraints (in additional to the original constraints):x(0) = x0(0) + e_0rx(0) = x0(0) - e_0l......Then minimize e_0l + e0r + e_1l + e_1r + ...So the LP example so be sufficient:https://www.alglib.net/translator/man/manual.cpp.html#example_minlp_basic

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