Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization
The choice of training instances significantly impacts the performance of automated algorithm selection models for numerical black-box optimization problems.
A Numerical Method for Computing Geodesics on the Stiefel Manifold
This paper presents a single shooting method with an approximate Fréchet derivative for efficiently computing geodesics on the Stiefel manifold.
Accelerating Ill-Posed Inverse Problem Solving with an Adaptive Heavy Ball Method
The authors propose an adaptive heavy ball method to efficiently solve ill-posed inverse problems, both linear and nonlinear, by incorporating a strongly convex regularization function to detect the desired solution features. The method adaptively chooses the step-sizes and momentum coefficients to achieve acceleration over the standard Landweber-type method.
Efficient Numerical Methods for Solving a Class of Non-Potential Mean-Field Games
The authors propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games, where the finite-difference scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. They prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the primal-dual hybrid gradient (PDHG) algorithm.
Efficient Combination Technique for Optimal Control of Random Partial Differential Equations
The authors present a combination technique (CT) to efficiently solve optimal control problems constrained by random partial differential equations. The CT combines solutions computed on coarse spatial grids and with few quadrature points to obtain an accurate approximation, while drastically reducing the computational cost compared to standard approaches.
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