herclau Try also option penaltymethod=true. When Search routine cannot find feasible point or search directions this option can be helpful.

@herclau step=0.0001. Why you do not want to read help? The help page of DirectSearch package can be obtained by

 ?DirectSearch command.

@herclau step=0.0001. Why you do not want to read help? The help page of DirectSearch package can be obtained by

 ?DirectSearch command.

@herclau set option: evaluationlimit=10000

@herclau set option: evaluationlimit=10000

@acer The DirectSearch package does not use external-calling or the Compiler but it uses evalhf(). Method quadratic is good for quadratic functions but without constraints. Of course, specialized routines for LP and QP problems must be more fast, more realible and more effective than universal ones. So for pure QP problems specialized Optimization:-QPSolve command is preferable.

@Markiyan Hirnyk The .hdb files (Maple Helpe files), created by Maple 13, do not work in Maple 15 ? Is this true ?

@acer  Of course it is extreme example, the limit case for some continuous functions. For example: find root of the following equation

k:=100;
eq:=(x^2+1)*(1-exp(-k*sqrt(abs(x-Pi))))=0;
plot(lhs(eq),x=-1...2*Pi,numpoints=5000);

solve(eq);
fsolve(eq,x=3..4);
fsolve(eq,x=3.1415..3.1416);

with(DirectSearch):
SolveEquations(eq,[x=3..4]);
SolveEquations(eq,[x=3.14..3.2]);
SolveEquations(eq,[x=3..4], pointrange=[x=3..4], AllSolutions);

@acer  Of course it is extreme example, the limit case for some continuous functions. For example: find root of the following equation

k:=100;
eq:=(x^2+1)*(1-exp(-k*sqrt(abs(x-Pi))))=0;
plot(lhs(eq),x=-1...2*Pi,numpoints=5000);

solve(eq);
fsolve(eq,x=3..4);
fsolve(eq,x=3.1415..3.1416);

with(DirectSearch):
SolveEquations(eq,[x=3..4]);
SolveEquations(eq,[x=3.14..3.2]);
SolveEquations(eq,[x=3..4], pointrange=[x=3..4], AllSolutions);

@Christopher2222 Yes, no real roots, but many complex ones. We can obtain some complex roots by DirectSearch package:

with(DirectSearch):
eq:=abs(2^(cos(x+I*y))-5)=0;
sol:=SolveEquations(eq,tolerances=10^(-14),AllSolutions,solutions=10);

Verification:

evalf[15](eval(lhs(eq),sol[1,3]));
evalf[15](eval(lhs(eq),sol[2,3]));

@Christopher2222 Yes, no real roots, but many complex ones. We can obtain some complex roots by DirectSearch package:

with(DirectSearch):
eq:=abs(2^(cos(x+I*y))-5)=0;
sol:=SolveEquations(eq,tolerances=10^(-14),AllSolutions,solutions=10);

Verification:

evalf[15](eval(lhs(eq),sol[1,3]));
evalf[15](eval(lhs(eq),sol[2,3]));

If I were  Christopher2222 I would not take bets :)

If I were  Christopher2222 I would not take bets :)

If you add option remember in procedure PDE the DataFit command will be near as fast as the first variant with F. Of course, you must change procedure declaration FuncH:=proc(p,pi,d,ttt) on FuncH:=proc(ttt,p,pi,d).

If you add option remember in procedure PDE the DataFit command will be near as fast as the first variant with F. Of course, you must change procedure declaration FuncH:=proc(p,pi,d,ttt) on FuncH:=proc(ttt,p,pi,d).