The SQP method - userdefined problem

Please give your problem an identification name, alphanumeric and underscores allowed, no blank or comma inserted!

Please specify the number of variables n
n= Important: 1 <= n <= 100 !

Please specify here the number of inequality constraints ng and equality constraints nh:
ng=
nh=
Important : 0 < ng, nh and nh + ng <= 300 !
If nh=0 then write ''HXI=0.d0'' in the input field for the equations and if ng=0 then ''GXI=0.d0'' in the respective field for the inequalities

The function codes you specify here must obey the restrictive rules of JAKEF , hence old fashioned fortran. see under FORTRAN how to

Please specify here the piece of code for computing the objective function, following the rules specified here
Important: the variables are x(j), j=1,...,n, the result is fx.
You may use local variables y(1),....,y(100), already initialized by zero, the integer variables i, j, k and the logicals bool1, bool2 and bool3.
You cannot define other variables yourself.

Please type the piece of code for computing your inequality constraints (if any) in the textarea below, following the rules specified here.
Important : the variable names are i and x(j), j=1,...,n, the result is always gxi.
You may use local variables y(1),....,y(100), already initialized by zero, the integer variables j, k and the logical variables bool1, bool2 and bool3.
You cannot define local variables yourself.
Attention : usually you will have many inequality constraints and which one is to be computed is specified by i. The name of the result however is always gxi. You must never change i or x, otherwise nonsense will occur.
How this is managed can be seen from the example below, which is for ng=5

Here you have the possibility to declare your inequality constraints which have the form ''constant + integer constant*variable'' or ''constant-integer constant*variable'' as bound constraints, which get special treatment in some situations.
Each such constraint is characterized by three integers: its index i, (the value by which it is selected), the index of the variable, x(j), and the integer constant which multiplies it. You may leave this field empty. The entries below are for the example above, where only bounds are present.

Please type the piece of code for computing the equality constraints in the textarea below. Important: the input variables are i and x(j), j=1,...,n, the result is hxi.
There will be different branches for this, normally, depending on i. How to do this is described in detail here, but it may suffice to look at the example below, which is for two equality constraints. Never change x or i, we have ''call by name'' here! You may make use of local variables (for intermediate storage e.g.) y(1),....,y(100), already initialized with 0, the counting variables j, k and the logicals bool1, bool2, bool3. Remember the special role of the first 6 columns! You cannot define variables yourself.

Please type your initial guess for the solution in the following textarea

Please specify the amount of intermediate output
only final results
display iteration details

Your choice of the algorithmic parameters:
Default values
My own choice:

tau0:, upper bound for infeasibility, must be > 0
tau0 =

del0: upper bound for δ (determines the active set)
del0 = Important : 0 < del0

delmin: lower bound for δ . Any inequality with value less than delmin will be considered ''active''.
delmin = Important: 0 < delmin < del0

ε: >= 2.2e-16, recommended >= 1.0e-7, the parameter indicating ''sufficient accuracy''
epsx =

smallw: >= 2.2e-16 bound for the dual infeasibility
smallw =

rho: bound for indicating ''rank deficient active set''
rho =

rho1: bound for indicating singular Hessian
rho1 =

Do you want a contour plot of the penalty function?
This is done in the (x(i),x(k)) plane over the rectangle [x(i)-xdecr1,x(i)+xincr1]*[x(k)-xdecr2,x(k)+xincr2],
with the other components of x held at their current (optimal) values.
Of course i < > k !
no contour plot
contourplot request
i =
k =
xdecr1 =
xincr1 =
xdecr2 =
xincr2 =

treatment of bounds:
The bounds will not be violated in plotting.
Plot on the given area

Warning!!! - This may take some time.

Click on "evaluate", in order to submit your input.

problem descriptions

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26.08.2017