conmax_solver Derived Type

private subroutine conmax(me, ioptn, nparm, numgr, itlim, fun, ifun, pttbl, iptb, Indm, iwork, liwrk, work, lwrk, iter, param, error)

CONMAX consists of two programs for solving the problem

Arguments

private subroutine muller(me, Ioptn, Nparm, Numgr, Dvec, Fun, Ifun, Pttbl, Iptb, Indm, Zwork, Tolcon, Iphse, Iwork, Liwrk, Work, Lwrk, Parwrk, Err1, p1, f1, Procor, Emin)

In this subroutine we are given a base vector zwork, a direction vector dvec, a scalar procor with emin = f(procor) = (the maximum type -2 and -1 error with parameters zwork + procor*dvec) < -tolcon, and a scalar p1 with p1 < procor and f1 = f(p1) > tolcon. we do a revised mullers method approach (with a solution contained in a shrinking interval) to attempt to adjust procor so that -tolcon <= f(procor) <= tolcon, but if we are not successful we return with the leftmost procor found satisfying emin = f(procor) < -tolcon on the theory that overcorrection is better than no correction. note that when corrct calls this subroutine it will have lumped the type -1 constraints in with the type -2 constraints using jcntyp, which is carried through this subroutine into subroutine ercmp1 in iwork.

Arguments

private subroutine searsl(me, Ioptn, Numgr, Nparm, Prjlim, Tol1, x, Fun, Ifun, Pttbl, Iptb, Indm, Param, Error, Rchdwn, Mact, Iact, Iphse, Unit, Tolcon, Rchin, Itypm1, Itypm2, Iwork, Liwrk, Work, Lwrk, Err1, Parprj, Projct, Emin, Emin1, Parser, Nsrch)

This subroutine uses a modified quadratic fitting process to search for the minimum of a function f. it requres an initial guess in projct, a tolerance tol1 on the search interval length, an upper bound prjlim on the minimizing point (which should be set very large if no upper bound is desired), and a way to compute f(x) for a given x. the subroutine will print a warning and return if it would need to compute f more than initlm times in the initialization or more than nadd additional times in the main part of the program. when the subroutine returns, it will have put the minimum location in projct, the minimum f value in emin, the f value for the initial projct in emin1, and the number of times it computed f in nsrch.

Arguments

subroutine func(me, Nparm, Numgr, Pttbl, Iptb, Indm, Param, Ipt, Indfn, Icntyp, Confun) Prototype

Interface for the fnset function.

The first eight variables in the calling sequence for fnset are for input to fnset, with the first five variables being exactly as the user set them in the driver program. if the ten thousands digit of ioptn was set to 0, fnset should be written to place the appropriate values in icntyp and confun using the parameters in param, as follows:

• icntyp(ipt) = the type of the ipt(th) constraint (i.e. 2, 1, -1, or -2), or the user can set icntyp(ipt)=0 as a signal to ignore constraint ipt.

• confun(ipt,1) = the appropriate value as discussed above. (this can be left undefined if icntyp(ipt)=0.)

if indfn=1 (which is the only possibility other than indfn=0) then in addition to the above, for j=1,...,nparm, fnset should compute

confun(ipt,j+1) = the value of the partial derivative with respect to param(j) of the function whose value was computed in confun(ipt,1) (unless icntyp(ipt)=0, in which case these values need not be computed).

Arguments

private subroutine ercmp1(me, Ioptn, Nparm, Numgr, Fun, Ifun, Pttbl, Iptb, Indm, Param, Icnuse, Iphse, Iwork, Liwrk, Confun, Icntyp, Ipmax, Ismax, Error)

Arguments

private subroutine rkcon(me, Ioptn, Nparm, Numgr, Fun, Ifun, Pttbl, Iptb, Indm, Tolcon, Rchin, Iter, Irk, Ityp2, Ityp1, Itypm1, Itypm2, Icntyp, Projct, Rchdwn, Nstep, Iphse, Enchg, Enc1, Pmat, Funtbl, Iwork, Liwrk, Work, Lwrk, Iact, Actdif, Parprj, Parser, Xrk, Err1, Confun, Isucc, Param, Error)

Arguments

private subroutine slpcon(me, Ioptn, Nparm, Numgr, Fun, Ifun, Pttbl, Iptb, Indm, Tolcon, Rchin, Irk, Itypm1, Itypm2, Icntyp, Rchdwn, Numlim, Itersl, Prjslp, Funtbl, Iyrct, x, Mact1, Iact1, Jcntyp, Iphse, Enchg, Iwork, Liwrk, Work, Lwrk, Parser, Isucc, Param, Error)

Arguments

private subroutine corrct(me, Ioptn, Nparm, Numgr, Fun, Ifun, Pttbl, Iptb, Indm, Icntyp, Unit, Tolcon, Rchin, Error, Mact, Iact, Projct, Iphse, Iwork, Liwrk, Work, Lwrk, Parwrk, Err1, Dvec, Pmat, Confun, Zwork, Jcntyp, Parprj, Icorct)

This subroutine determines whether parprj violates any type -2 or type -1 (i.e. standard) constraints by more than tolcon, and if so it attempts to correct back to the feasible region. if it is successful it sets icorct=0 and replaces parprj by the corrected vector. if it is not successful it sets icorct=1 and leaves parprj unchanged. if no correction was needed it sets icorct=-1 and leaves parprj unchanged.

Arguments

private subroutine rkpar(me, Ioptn, Numgr, Nparm, Icntyp, Mactrk, Iact, Actdif, Projct, Param, Fun, Ifun, Pttbl, Iptb, Indm, Vder, Pmat, Ncor, s, Itypm1, Itypm2, Unit, Tolcon, Rchin, Nstep, Error, Iphse, Iwork, Liwrk, Work, Lwrk, Confun, Vdern, Vders, Wvec, Parprj, Ifrkpr)

This subroutine computes a parameter vector parprj using fourth order runge kutta with h=-projct. h is negative since we want to approximate the parameters resulting from decreasing w by abs(h). if we do nstep steps then h=-projct/nstep.

Arguments

private subroutine searcr(me, Ioptn, Nparm, Numgr, Dvec, Fun, Ifun, Pttbl, Iptb, Indm, Zwork, Tolcon, Iphse, Iwork, Liwrk, Work, Lwrk, Parwrk, Err1, p1, f1, Procor, Emin, Isrcr)

This subroutine uses a modified quadratic fitting process to search for a projection factor procor for which the maximum of the left sides of the type -2 and -1 constraints evaluated at zwork + procor*dvec is <= tolcon. note that when corrct calls this subroutine it will have lumped the type -1 constraints in with the type -2 constraints using jcntyp, which is carried through this subroutine into subroutine ercmp1 in iwork. if searcr is able to force this maximum <= tolcon it will return with isrcr=0, with the minimum value found for the maximum in emin, with the corresponding projection factor in procor, with the number of times the maximum was computed in nsrch, and with the closest point found to the left with the maximum > tolcon in (p1,f1). the subroutine will begin by computing the maxima for procor = 1.0, 0.5, and 2.0, and if none of these maxima is <= tolcon and it is not the case that the maximum at 1.0 is <= the other two maxima the subroutine will return with the warning isrcr=1. the subroutine will also return with isrcr=1 if it would need to compute f more than limscr times, or the search interval length drops below tol1, or the quadratic fit becomes too flat. even in the event of a return with isrcr=1, emin, procor, and nsrch will be as above.

Arguments

private subroutine derst(me, Ioptn, Nparm, Numgr, Pttbl, Iptb, Indm, Param, Ipt, Param1, v, Kcntyp, Confun)

This subroutine uses fnset to compute confun(i,1) and the partial derivatives of the function whose value is in confun(i,1) for certain value(s) of i. note that we do not want the icntyp computed by fnset to override the icntyp (or jcntyp) carried into this subroutine in icntyp, so we use kcntyp when we call fnset. (the icntyp computed by fnset was stored earlier through a call to ercmp1 from conmax.)

Arguments

private subroutine setu1(me, Ioptn, Numgr, Nparm, Numin, Rchin, Pttbl, Iptb, Indm, Fun, Ifun, Funtbl, Cofbnd, Param, Icntyp, Rchdwn, Error, Mact1, Iact1, Bndlgt, Iyrct, Iphse, Iwork, Liwrk, Work, Lwrk, Confun, Iact, v, m)

This subroutine sets up v for slnpro to solve a modified linearized (about the old parameters in param) version of our problem.

Arguments

private subroutine pmtst(me, Ioptn, Numgr, Nparm, Param, Icntyp, Mactrk, Iact, Pttbl, Iptb, Indm, Actdif, Iphse, Iwork, Liwrk, Work, Lwrk, Confun, Pmat)

This subroutine sets up the (nparm+1) by mactrk matrix pmat. for 1 <= j <= mactrk, the top nparm elements of column j of pmat will contain the negative of the gradient of active constraint j (if constraint j is of type 2, i.e. of the form abs(f(x) - f(parwrk,x)) <= w, the left side will be treated as f(x) - f(parwrk,x) if this quantity is nonnegative and will be treated as f(parwrk,x) - f(x) otherwise). the (nparm+1)st row of pmat will contain actdif, the right side of the inequalities gradient.vector >= actdif.

Arguments