How can I model GreaterEqual and LessEqual as LinearInequalityConstraint

[axkr]

As far as I understand the API, I can model the Greater and Less relations in a LinearInequalityConstraint for the SQPOptimizerGM optimizer.
@roccafrancesco, @Serrof: how can I model the GreaterEqual and LessEqual relations?

[roccafrancesco]

hi
inequality constraints should be understood as greaterequal.
I would like to remark that, at moment, SQPOptimizerGM work starting from feasibility solution. If you don't have good starting point i suggest to use SQPOptimizerS.

[axkr]

@roccafrancesco

If you don't have good starting point i suggest to use SQPOptimizerS.

I've now implemented your suggestion here:

• axkr/symja_android_library@87857a8

The conversion of the linear binary relations is implemented here:

• https://github.com/axkr/symja_android_library/blob/ce7ae3cde2a7809372c00e11f9bae45d766f9bc2/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/FindMinimum.java#L213

LessEqual and Less use the same conversions at the moment.
GreaterEqual and Greater use also the same conversions at the moment.

Maybe you can also suggest some typically "default values", which should be set in the constructor of SQPOptimizerS ?
And if the user doesn't set a preferred method, which method should be used as default?
(Currently "Powell", "ConjugateGradient" and "SequentialQuadratic" are available)

You can test FindMinimum and FindMaximum in the demonstration web interface:

• https://matheclipse.org/input?i=FindMinimum%28%7Bx%2By%2C3%2Ax%2B2%2Ay%20%3E%3D%207%20%2C%20x%20%3E%3D%200%20%2C%20y%20%3E%3D%200%7D%2C%20%7Bx%2C%20y%7D%2CMethod%20-%3E%22SequentialQuadratic%22%29

[roccafrancesco]

class SQPOption contain already defaul values. Anyway you could play with eps and convCriteria leaving unchenged the other parameters.
There is not a preferred method. Depened of the nature of the problem.

In the example https://matheclipse.org/i](https://matheclipse.org/input?i=FindMinimum%28%7Bx%2By%2C3%2Ax%2B2%2Ay%20%3E%3D%207%20%2C%20x%20%3E%3D%200%20%2C%20y%20%3E%3D%200%7D%2C%20%7Bx%2C%20y%7D%2CMethod%20-%3E%22SequentialQuadratic%22%29)
problem is linear and you could use a linear method SimplexSolver.