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newuoa_mat.m
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newuoa_mat.m
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% N.B.: This version was implemented based on an earlier version of the modern Fortran
% implementation, with the help of Mr. Galann Pennec.
%
% NEWUOAM provides the MATLAB implementation of M. J. D. Powell's NEWUOA algorithm described in
%
% M. J. D. Powell, The NEWUOA software for unconstrained optimization
% without derivatives, In Large-Scale Nonlinear Optimization, eds. G. Di
% Pillo and M. Roma, pages 255--297, Springer, New York, US, 2006
%
% NEWUOA seeks the least value of a function of many variables, by a
% trust region method that forms quadratic models by interpolation.
% There can be some freedom in the interpolation conditions, which is
% taken up by minimizing the Frobenius norm of the change to the second
% derivative of the quadratic model, beginning with a zero matrix.
%
% Coded by Zaikun Zhang in July 2020 based on Powell's Fortran 77 code
% and the NEWUOA paper.
%
% Last Modified: Thursday, July 22, 2021 AM10:56:17
function [x, f, exitflag, nf, xhist, fhist] = newuoa_mat(calfun, x, rhobeg, rhoend, eta1, eta2, ...
gamma1, gamma2, ftarget, maxfun, npt, iprint, maxhist, output_xhist, debugflag)
% A detailed introduction to the arguments is as follows.
%
% CALFUN
% Input, function handle.
% CALFUN(X) should evaluate the objective function at the given
% vector X and set the value to the scalar F. It
%
% X
% Input and output, vector.
% As an input, X should be an N dimensional vector that contains the
% initial values of the variables, N being the dimension of the problem.
% As an output, X will be set to an approximate minimizer.
%
% F
% Output, scalar.
% F will be set to the objective function value of the X at exit.
%
% NF
% Output, scalar.
% NF will be set to the number of function evaluations at exit.
%
% RHOBEG, RHOEND
% Inputs, scalars, default: RHOBEG = 1, RHOEND = 10^-6.
% RHOBEG and RHOEND must be set to the initial and final values of a
% trust region radius, so both must be positive with RHOEND <= RHOBEG.
% Typically RHOBEG should be about one tenth of the greatest expected
% change to a variable, and RHOEND should indicate the accuracy that is
% required in the final values of the variables.
%
% FTARGET
% Input, scalar, default: - Infinity.
% FTARGET is the target function value. The algorithm will terminate
% when a point with a function value <= FTARGET is found.
%
% MAXFUN
% Input, scalar, default: consts(maxfun_dim_dft)*N with
% consts(maxfun_dim_dft) defined in the consts.m.
% MAXFUN is the maximal number of function evaluations.
%
% NPT
% Input, scalar, default: 2N + 1.
% NPT is the number of interpolation conditions for each trust region
% model. Its value must be in the interval [N+2, (N+1)(N+2)/2].
%
% IPRINT
% Input, scalar, default: 0.
% The value of IPRINT should be set to 0, 1, -1, 2, -2, 3, or -3, which
% controls how much information will be printed during the computation:
% 0: there will be no printing;
% 1: a message will be printed to the screen at the return, showing the
% best vector of variables found and its objective function value;
% 2: in addition to 1, each new value of RHO is printed to the screen,
% with the best vector of variables so far and its objective function
% value;
% 3: in addition to 2, each function evaluation with its variables will
% be printed to the screen;
% -1, -2, -3: the same information as 1, 2, 3 will be printed, not to
% the screen but to a file named NEWUOA_output.txt; the file will be
% created if it does not exist; the new output will be appended to
% the end of this file if it already exists. Note that IPRINT = -3 can
% be costly in terms of time and space.
%
% ETA1, ETA2, GAMMA1, GAMMA2
% Input, scalars, default: ETA1 = 0.1, ETA2 = 0.7, GAMMA1 = 0.5,
% and GAMMA2 = 2.
% ETA1, ETA2, GAMMA1, and GAMMA2 are parameters in the updating scheme
% of the trust region radius as detailed in the subroutine TRRAD in
% trustregion.f90. Roughly speaking, the trust region radius is contracted
% by a factor of GAMMA1 when the reduction ratio is below ETA1, and
% enlarged by a factor of GAMMA2 when the reduction ratio is above ETA2.
% It is required that 0 < ETA1 <= ETA2 < 1 and 0 < GAMMA1 < 1 < GAMMA2.
% Normally, ETA1 <= 0.25. It is NOT recommended to set ETA1 >= 0.5.
%
% XHIST, FHIST, MAXHIST
% XHIST: Output, rank 2 array;
% FHIST: Output, rank 1 array;
% MAXHIST: Input, scalar, default: MAXFUN
% XHIST will output the history of iterates, while FHIST will output the history function
% values. MAXHIST should be a nonnegative integer, and XHIST/FHIST will output only the last
% MAXHIST iterates and/or the corresponding function values. Therefore, MAXHIST = 0 means
% XHIST/FHIST will output nothing, while setting MAXHIST = MAXFUN ensures that XHIST/FHIST
% will output all the history. The size of XHIST at exit will be (N, min(NF, MAXHIST));
% the size of FHIST at exit will be min(NF, MAXHIST).
%
% Important Notice:
% Setting MAXHIST to a large value can be costly in terms of memory.
% For instance, if N = 1000 and MAXHIST = 100, 000, XHIST will take
% reset to a smaller value if the memory needed for XHIST and/or FHIST
% exceeds consts(maxmemory) defined in consts.m
% Use XHIST, FHIST, and MAXHIST with caution!!!
%
% INFO
% Output, scalar.
% INFO is the exit flag. It can be set to the following values defined in infos.m:
% infos(small_tr_radius): the lower bound for the trust region radius is reached;
% infos(ftarget_achieved): the target function value is reached;
% infos(trsubp_failed): a trust region step failed to reduce the quadratic model;
% infos(maxfun_reached): the objective function has been evaluated MAXFUN times;
% infos(nan_x): NaN occurs in x;
% infos(nan_inf_f): the objective function returns NaN or nearly infinite value;
% infos(nan_model): NaN occurs in the models.
% Replace any NaN or Inf in X by 0.
x(isnan(x) | isinf(x)) = 0;
maxfhist = maxhist;
maxxhist = double(output_xhist)*maxhist;
%-------------------- Call NEWUOB, which performs the real calculations. ----------------------%
[x, nf, f, fhist, xhist, exitflag] = newuob(calfun, iprint, maxfun, npt, eta1, eta2, ...
ftarget, gamma1, gamma2, rhobeg, rhoend, x, maxfhist, maxxhist, debugflag);
%----------------------------------------------------------------------------------------------%
xhist = xhist(:, 1:min(nf, maxxhist));
fhist = fhist(1:min(nf, maxfhist));
end