5 papers
Quadratic Optimization over Probability Measures with Coupling Constraints
Hoang Anh Tran, Yong Sheng Soh
We consider solving an optimization instance in which the objective is quadratic and where the decision variable is a probability measure. Our class of problems are motivated by ap…
On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
Hoang Anh Tran, Toh Kim-Chuan
The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial.…
Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity
Hoang Anh Tran, Binh Tuan Nguyen, Yong Sheng Soh
The Gromov-Wasserstein (GW) problem is an extension of the classical optimal transport problem to settings where the source and target distributions reside in incomparable spaces,…
Sum-of-Squares Hierarchy for the Gromov Wasserstein Problem
Hoang Anh Tran, Binh Tuan Nguyen, Yong Sheng Soh
The Gromov-Wasserstein (GW) problem is a variant of the classical optimal transport problem that allows one to compute meaningful transportation plans between incomparable spaces.…
Convergence rates of S.O.S hierarchies for polynomial semidefinite programs
Hoang Anh Tran, Kim-Chuan Toh
We introduce an S.o.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite inequality. Our approach inv…