SLSQP optimizer, multistart Cobyla, enhanced compatibility checks

[adekusar-drl]

Summary

Added a new optimizer to the Qiskit optimization module that wraps already existing SLSQP solver.

Details and comments

Changes:

• New class added: qiskit.optimization.algorithm.SlsqpOptimizer
• Added methods evaluate_gradient to LinearExpression, QuadraticExpression, QuadraticObjective
• Added new tests for the new optimizer, added evaluate_gradient methods

@stefan-woerner please pay attention to this PR since I added methods to the base classes.

[woodsp-ibm]

Can I ask you add a reno yaml file - the changes are being managed via this tool now. There is information on how to install in contributing file https://github.com/Qiskit/qiskit-aqua/blob/master/CONTRIBUTING.md#release-notes

[adekusar-drl]

Can I ask you add a reno yaml file - the changes are being managed via this tool now. There is information on how to install in contributing file https://github.com/Qiskit/qiskit-aqua/blob/master/CONTRIBUTING.md#release-notes

Done

[adekusar-drl]

@woodsp-ibm, @stefan-woerner
There are a few changes, so please take a look at the PR again.
What's new now:

1. MultiStartOptimizer handles a multi start for local optimizers like SLSQP and COBYLA. The way how initial guesses are sampled is changed after a discussion with the team. Now they are guesses uniformly with some clipping if variables are unbounded.
2. SlsqpOptimizer now extends MultiStartOptimizer.
3. Added multi start support to COBYLA as Stefan mentioned.
4. Compatibility checks are now different.
   In optimizers there's a line

self._verify_compatibility(problem)

And in the OptimizationAlgorithm there is

    def _verify_compatibility(self, problem: QuadraticProgram) -> None:
        msg = self.get_compatibility_msg(problem)
        if msg:
            raise QiskitOptimizationError('Incompatible problem: {}'.format(msg))

We can enforce this compatibility check for every optimizer as now it is up to optimizers to call this new method directly. Such enforcement will require more changes in the optimizers, more abstractions, etc.

[adekusar-drl]

The PR was blocked by the error introduced outside of the PR.