arXiv subjects

Thi Lan Dinh

Publications and source records attributed to Thi Lan Dinh.

5 recordsLinked to original sources

arXiv2026

Algorithmic approaches to avoiding bad local minima in nonconvex inconsistent feasibility

We report on the use of algorithms to avoid or move away from ``bad'' local minima in nonconvex optimization. Our study is phenomenological and empirical, focusing on the performance of cyclic projections, the cyclic relaxed Douglas-Rachford algorithm, and relaxed Douglas-Rachford splitting on the product space for orbital tomographic imaging from angle-resolved photon emission spectroscopy (ARPES) measurements, with both synthetic and laboratory data. Cyclic projections and Douglas-Rachford on the product space are both well-known methods, but cyclic relaxed Douglas-Rachford was only recently fully characterized in a companion paper to the present study. Only one other study of note has investigated the performance of all three of these algorithms for inconsistent nonconvex feasibility. We show that the relaxed Douglas-Rachford algorithm on the product space, while exhibiting very poor convergence rates, can be used to filter out bad local minima from all cyclic algorithms. Our numerical experiments lead to the following recommendation: run cyclic projections to find some fixed point, and from this fixed point run relaxed Douglas-Rachford algorithm on the product space with as large a relaxation parameter as is numerically stable in order to escape poor local minima. This advice runs counter to the current practice for phase retrieval, where a Douglas-Rachford-type algorithm is run for several iterations, and then cyclic projections is used to ``clean up'' the images.

math.OC↗

arXiv2025

Table-top three-dimensional photoemission orbital tomography with a femtosecond extreme ultraviolet light source

Following electronic processes in molecules and materials at the level of the quantum mechanical electron wavefunction with angstrom-level spatial resolution and with full access to its femtosecond temporal dynamics is at the heart of ultrafast condensed matter physics. A breakthrough invention allowing experimental access to electron wavefunctions was the reconstruction of molecular orbitals from angle-resolved photoelectron spectroscopy data in 2009, termed photoemission orbital tomography (POT). This invention puts ultrafast three-dimensional (3D) POT in reach, with many new prospects for the study of ultrafast light-matter interaction, femtochemistry and photo-induced phase transitions. Here, we develop a synergistic experimental-algorithmic approach to realize the first 3D-POT experiment using a short-pulse extreme ultraviolet light source. We combine a new variant of photoelectron spectroscopy, namely ultrafast momentum microscopy, with a table-top spectrally-tunable high-harmonic generation light source and a tailored algorithm for efficient 3D reconstruction from sparse, undersampled data. This combination dramatically speeds up the experimental data acquisition, while at the same time reducing the sampling requirements to achieve complete 3D information. We demonstrate the power of this approach by full 3D imaging of the frontier orbitals of a prototypical organic semiconductor absorbed on pristine Ag(110).

cond-mat.mtrl-sci↗

arXiv2025

Cyclic Relaxed Douglas-Rachford Splitting for Inconsistent Nonconvex Feasibility

We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by Borwein and Tam [2014] and the classical cyclic projections algorithm. We characterize the fixed points of the cyclic relaxed Douglas-Rachford algorithm and show the relation of the {\em shadows} of these fixed points to the fixed points of the cyclic projections algorithm. Finally, we provide conditions that guarantee local quantitative convergence estimates in the nonconvex, inconsistent setting.

math.OC↗

arXiv2024

A minimalist approach to 3D photoemission orbital tomography: algorithms and data requirements

Photoemission orbital tomography provides direct access from laboratory measurements to the real-space molecular orbitals of well-ordered organic semiconductor layers. Specifically, the application of phase retrieval algorithms to photon-energy- and angle-resolved photoemission data enables the direct reconstruction of full 3D molecular orbitals without the need for simulations using density functional theory or the like. A major limitation for the direct approach has been the need for densely-sampled, well-calibrated 3D photoemission patterns. Here, we present an iterative projection algorithm that completely eliminates this challenge: for the benchmark case of the pentacene frontier orbitals, we demonstrate the reconstruction of the full orbital based on a dataset containing only four simulated photoemission momentum measurements. We discuss the algorithm performance, sampling requirements with respect to the photon energy, optimal measurement strategies, and the accuracy of orbital images that can be achieved.

cond-mat.mtrl-sci↗

arXiv2023

Comparing different subgradient methods for solving convex optimization problems with functional constraints

We consider the problem of minimizing a convex, nonsmooth function subject to a closed convex constraint domain. The methods that we propose are reforms of subgradient methods based on Metel--Takeda's paper [Optimization Letters 15.4 (2021): 1491-1504] and Boyd's works [Lecture notes of EE364b, Stanford University, Spring 2013-14, pp. 1-39]. While the former has complexity $\mathcal{O}(\varepsilon^{-2r})$ for all $r> 1$, the complexity of the latter is $\mathcal{O}(\varepsilon^{-2})$. We perform some comparisons between these two methods using several test examples.

math.OC↗