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where k is the number of the objective functions, m is the number of the nonlinear constraints, decision vector x and its lower and upper bounds are n-dimensional vectors, b is an l-dimensional vector and A is an l x n-dimensional matrix of linear constraint coefficients.
| + | plus |
| - | minus |
| * | multiplication |
| / | division |
| ** or ^ | exponent |
| NEG | negative |
| function | argument | description | |
|---|---|---|---|
| COS | (double x) | cosine function | |
| SIN | (double x) | sine function | |
| COSH | (double x) | hyperbolic cosine function | |
| SINH | (double x) | hyperbolic sine function | |
| ACOS | (double x) | arc cosine function | |
| ASIN | (double x) | arc sine function | |
| ATAN | (double x) | arc tangent function | |
| function | argument(s) | description |
|---|---|---|
| LOG | (double x) | natural logarithm |
| LOG10 | (double x) | common logarithm |
| EXP | (double x) | exponential function e**x |
| SQRT | (double x) | square root |
| ABS | (double x) | absolute value |
| SIGN | (double x, double y) | abs(x) if y >= 0, - abs(x) if y < 0 |
| MAX | (double x, double y,...) | the largest value of the arguments |
| MIN | (double x, double y,...) | the smallest value of the arguments |
If lowest or highest values of the functions are known,
they can be given in their respective fields. If these fields are
left blank, the WWW-NIMBUS system calculates
those values automatically. Note that either both or neither
of the values must be given.
NOTE:
Please avoid using non-standard characters in the names, since they can cause unexpected system behavior. The safe characters are alphabets between a and z , A and Z.
If your variables are unbounded you can use values INF or -INF to represent the fact.Autofill
When this option is set, all non-defined variable fields will be filled with values found above (in the same column). Therefore, the first variable definition must exist at whole.NOTE1:
Please avoid using non-standard characters in the names, since they can cause unexpected system behavior. The safe characters are alphabets between a and z , A and Z.NOTE2:
Variables can be specified to be discrete. In this case, the word 'discrete' means integer. The selection can be done by checking the 'Integer values' - check-box beside the variable definition field. If integer variables are used, their bounds must be defined as integers, too.TIP2:
When inserting very small or very big numeric values one may find it useful to use exponential format instead of the normal format. For example, it is easier to insert a value 1.2E+8 instead of the value 120000000. Small values can be defined the same way by defining the exponent value as negative (e.g. 0.00018 = 1.8E-4 ).
Linear constraints can be either equality or inequality constraints. The default constraint type is inequality, but it can be changed by the the drop-down list using the symbol <= for inequality and symbol = for the equality constraints.
If the feasible region is really empty, the conflicting constraints can be modeled as objective functions. An example of this kind of modeling can be found in Miettinen, K., Mäkelä M.M., Männikkö T.: Nondifferentiable Multiobjective Optimizer NIMBUS Applied to an Optimal Control Problem of Continuous Casting, Report 22/1996, University of Jyväkylä Department of Mathematics, Laboratory of Scientific Computing
In the next version of the WWW-NIMBUS, the user is informed if floating point errors cause failure in the optimization process.
If the subgradient information is available, and a global optimizer is selected, the local optimizer is always used after the global one. The subgradient information might not be available when the user gives the problem in a Fortran format.
NOTE: If the problem is saved from this page, the operation "Open Problem and Modify It" is the only option available when re-opening the saved problem.