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Partial derivatives Description Nonlinear example demonstrating the cost of numerical derivatives Further explanation of this example:
'Xpress NonLinear Reference Manual'
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xnlp_derivatives.mos ! XNLP example demonstrating the cost of numerical derivatives ! ! This example solves the same simple problem several times using different ! differentiation techniques and solvers ! ! This example demonstrates a particular non-linear optimization concept as related ! to Xpress NonLinear. ! The version of the example is for Xpress 7.5. ! ! (c) 2013-2024 Fair Isaac Corporation ! author: Zsolt Csizmadia model mmxnlp_nlp_duals uses "mmxnlp", "mmsystem"; ! Scaling parameter for problem size. parameters N = 200 end-parameters declarations R = 1..N x : array(R) of mpvar start, finish : real; end-declarations !setparam("xnlp_verbose",true) forall(i in R) do x(i) >= 1 - 1/i x(i) <= 1 + 1/i end-do Objective := sum(i in R) ( x(i)^3 ) ! Solve with a local solver to use derivatives setparam("XPRS_NLPSOLVER",1) ! Default solve usign analytical derivatives, expected to take no time write("Solve problem using analytical derivatives: ") start := gettime minimize(Objective) finish := gettime writeln(finish-start,"s") ! Use the first order solver SLP to solve the problem setparam("xnlp_solver",XNLP_SOLVER_XSLP) setparam("xslp_derivatives", 0) write("Solve problem using finite differences, 1st order solver: ") start := gettime minimize(Objective) finish := gettime writeln(finish-start,"s") ! Now resolve using second order numerical derivatives setparam("xnlp_solver",XNLP_SOLVER_KNITRO) ! Numerical derivatives here are enforced by the means of setting a control. ! However, the need for numerical derivatives can arise naturally from ! black-bock user functions setparam("xslp_derivatives", 0) write("Solve problem using finite differences, 2nd order solver: ") start := gettime minimize(Objective) finish := gettime writeln(finish-start,"s") ! Revert back to the second order Knitro solver, but approximate the Hessian ! matrix instead setparam("xnlp_solver",XNLP_SOLVER_KNITRO) setparam("xktr_param_hessopt", 2) ! BFGS approximation write("Solve problem using finite differences, 2nd order solver, BFGS: ") start := gettime minimize(Objective) finish := gettime writeln(finish-start,"s") end-model | |||||||||||

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