Tootfinder

Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto Gonz\'alez-Sanz, Marcel Nutz, Andr\'es Riveros Valdevenito
https://arxiv.org/abs/2509.08547

Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Here quadratic regularization means that transport couplings are penalized by the squared $L^2$ norm, or equivalently the $χ^2$ divergence. While a number of computational approaches have been shown to work in practice, quadratic regularization is analytically less tractable than entropic, and we are not aware of a previous theoretica…

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Xiaochao Luo, Chuntao Li, Xingzhao Huang, Jintian Lin, Renhong Gao, Yifei Yao, Yingnuo Qiu, Yixuan Yang, Lei Wang, Huakang Yu, Ya Cheng
https://arxiv.org/abs/2506.08615

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Narrow-linewidth lasers at short/visible wavelengths are crucial for quantum and atomic applications, such as atomic clocks, quantum computing, atomic and molecular spectroscopy, and quantum sensing. However, such lasers are often only accessible in bulky tabletop systems and remain scarce in integrated photonic platform. Here, we report an on-chip visible Brillouin-quadratic microlaser in a 117-um-diameter thin-film lithium niobate (TFLN) microdisk via dispersion engineering. Enabled by the ul…

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Jeremy Bertoncini, Alberto De Marchi, Matthias Gerdts, Simon Gottschalk
https://arxiv.org/abs/2509.07404

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive …

Complete classification of the Dehn functions of Bestvina-Brady groups
Yu-Chan Chang, Jer\'onimo Garc\'ia-Mej\'ia, Matteo Migliorini
https://arxiv.org/abs/2507.07566

Complete classification of the Dehn functions of Bestvina-Brady groups
We prove that the Dehn function of every finitely presented Bestvina-Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina-Brady groups from admitting a CAT(0) structure.

Quantum and Simulated Annealing-Based Iterative Algorithms for QUBO Relaxations of the Sparsest $k$-Subgraph Problem
Omkar Bihani, Roman Ku\v{z}el, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2509.08544

Quantum and Simulated Annealing-Based Iterative Algorithms for QUBO Relaxations of the Sparsest $k$-Subgraph Problem
In this paper, we introduce three QUBO (Quadratic Unconstrained Binary Optimization) relaxations for the sparsest $k$-subgraph (SkS) problem: a quadratic penalty relaxation, a Lagrangian relaxation, and an augmented Lagrangian relaxation. The effectiveness of these approaches strongly depends on the choice of penalty parameters. We establish theoretical results characterizing the parameter values for which the QUBO relaxations are exact. For practical implementation, we propose three iterative …

Unidimensional semi-discrete partial optimal transport
Adrien Cances, Hugo Leclerc
https://arxiv.org/abs/2509.08799 https://arxiv.org/pdf/2509.08799…

Unidimensional semi-discrete partial optimal transport
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises naturally in applications such as risk management, the modeling of crowd motion, and sliced partial transport algorithms for point cloud registration. Unlike higher-dimensional settings, the dual functional in the unidimensional case exhibits reduced regularity. To …

Dynamic Output-Feedback Controller Synthesis for Dissipativity from Noisy Input-State Data
Pietro Kristovi\'c, Andrej Joki\'c, Mircea Lazar
https://arxiv.org/abs/2507.06788

Dynamic Output-Feedback Controller Synthesis for Dissipativity from Noisy Input-State Data
In this paper we propose a dynamic output-feedback controller synthesis method for discrete-time linear time-invariant systems. The synthesis goal is to render closed-loop system dissipative with respect to a given generic unstructured quadratic supply rate, while the system dynamics is partially represented by input-state data corrupted by a bounded disturbance. The controller synthesis is performed with respect to all systems which are consistent with the available data, and it is formulated …

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
Liang Chen, Youyicun Lin, Yuxuan Zhou
https://arxiv.org/abs/2506.08988

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path. Building on the convex DOT model of Benamou and Brenier, we first properly reformulate its dual problem, discretized on a triangular mesh for space together with a staggered grid for time, to a linear second-order cone programming. Then the resulting finite-dimen…

Relationship between Maximum Principle and Dynamic Programming Principle for Risk-Sensitive Stochastic Optimal Control Problems with Applications
Huanqing Dong, Jingtao Shi
https://arxiv.org/abs/2507.06504

Relationship between Maximum Principle and Dynamic Programming Principle for Risk-Sensitive Stochastic Optimal Control Problems with Applications
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. As an application, a linear-quadratic risk-sensitive portfolio optimization problem in the financial market is discussed.

Provably data-driven projection method for quadratic programming
Anh Tuan Nguyen, Viet Anh Nguyen
https://arxiv.org/abs/2509.04524 https://arxiv.org/pdf/25…

Provably data-driven projection method for quadratic programming
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs…