Related papers: Inverse medium problems, saddle point formulation
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
The high-index saddle dynamics (HiSD) method [J. Yin, L. Zhang, and P. Zhang, {\it SIAM J. Sci. Comput., }41 (2019), pp.A3576-A3595] serves as an efficient tool for computing index-$k$ saddle points and constructing solution landscapes.…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
Learning diffusion bridge models is easy; making them fast and practical is an art. Diffusion bridge models (DBMs) are a promising extension of diffusion models for applications in image-to-image translation. However, like many modern…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
The inverse problems of particle neutral transport models have many important engineering and medical applications. Safety protocols, quality control procedures, and optical medical solutions can be developed based on inverse transport…
The most prevalent routine for camera calibration is based on the detection of well-defined feature points on a purpose-made calibration artifact. These could be checkerboard saddle points, circles, rings or triangles, often printed on a…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
Evaluating natural language generation systems is challenging due to the diversity of valid outputs. While human evaluation is the gold standard, it suffers from inconsistencies, lack of standardisation, and demographic biases, limiting…
In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent…
In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…