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getting started with Linear (or Quadratic) Programming http://forum.alglib.net/viewtopic.php?f=2&t=4439 
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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 function
and subject to this set of linear constraints:
If I can get this working, then I want to try alternative distance metrics
Eventually, I want to extend the problem to two dimensions, with each x a point in the xy 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:
https://www.alglib.net/translator/man/manual.cpython.html#example_minns_d_nlc For the L2 distance objective function which is quadratic I will try:
https://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 nonnegative 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_0r x(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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