Refactor quadreg

[zsteve]

Refactored quadreg to follow the conventions introduced for entropy-regularised OT.

This PR introduces QuadraticOT as a base problem type, with an associated solver QuadraticOTSolver. The method of Lorenz et al. (2019) is re-implemented as the algorithm QuadraticOTNewton.

The implementation of solve! currently relies on two functions descent_dir! and descent_step!, which respectively compute the descent direction (in terms of the dual variables u, v) and perform the descent step (currently following the Armijo step size rule in the Lorenz paper). This is actually quite general, and an alternative approach could be to rename QuadraticOT to a RegularizedOT type for optimal transport problems with arbitrary regularizer.

The previous implementation of quadreg relied on sparse matrices from SparseArrays, but passed between dense and sparse matrices repeatedly since transposes needed to be computed. The implementation in this PR uses dense matrices.

This could be implemented in future, but may also mean more work, since Sinkhorn maybe should then also inherit from RegularizedOT.

[coveralls]

Pull Request Test Coverage Report for Build 1162444673

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Details

• 122 of 124 (98.39%) changed or added relevant lines in 2 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.9%) to 97.654%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/quadratic_newton.jl	102	104	98.08%
<!--	Total:	122	124	98.39%	-->

Totals
Change from base Build 1161394375:	0.9%
Covered Lines:	666
Relevant Lines:	682

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💛 - Coveralls