The paper establishes existence, uniqueness up to equivalence, and stability for inverse optimal transport with Bregman regularization under cost-matrix assumptions, and gives an efficient BCD algorithm with linear convergence and element-wise Newton updates for quadratic penalties.
Convex analysis , volume 28
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Under relative interior assumptions, the infinite-dimensional dual of the GMP attains its optimum and each SOS relaxation is attained for supports that are compact basic semialgebraic sets with nonempty interior or real radical varieties defined by Gröbner bases.
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Well-Posedness and Efficient Algorithms for Inverse Optimal Transport with Bregman Regularization
The paper establishes existence, uniqueness up to equivalence, and stability for inverse optimal transport with Bregman regularization under cost-matrix assumptions, and gives an efficient BCD algorithm with linear convergence and element-wise Newton updates for quadratic penalties.
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Duality attainment and strict feasibility of the generalized moment problem and its relaxations
Under relative interior assumptions, the infinite-dimensional dual of the GMP attains its optimum and each SOS relaxation is attained for supports that are compact basic semialgebraic sets with nonempty interior or real radical varieties defined by Gröbner bases.