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We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…

Data Structures and Algorithms · Computer Science 2013-12-24 Boaz Barak , Jonathan Kelner , David Steurer

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has…

Applications · Statistics 2017-05-31 Anders Eklund , Martin A. Lindquist , Mattias Villani

In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle-point system for the VI model in question,…

Optimization and Control · Mathematics 2023-06-05 Lei Zhao , Daoli Zhu , Shuzhong Zhang

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

Optimization and Control · Mathematics 2019-11-07 Utkan Candogan , Yong Sheng Soh , Venkat Chandrasekaran

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…

Numerical Analysis · Mathematics 2024-06-12 Antonio Leitão , Joel C. Rabelo , Dirk A. Lorenz , Maximilian Winkler

Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized…

Information Theory · Computer Science 2019-05-15 Ali Bereyhi , Saba Asaad , Bernhard Gäde , Ralf R. Müller

In this paper, we derive differential conditions guaranteeing the orbital stability of nonlinear hybrid limit cycles. These conditions are represented as a series of pointwise linear matrix inequalities (LMI), enabling the search for…

Optimization and Control · Mathematics 2014-03-24 Justin Z. Tang , Ian R. Manchester

We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner and outer approximations for the region of attraction of a…

Optimization and Control · Mathematics 2018-11-06 Cedric Josz , Daniel K. Molzahn , Matteo Tacchi , Somayeh Sojoudi

We describe a paradigm for multiscale modeling that combines the Mori-Zwanzig (MZ) formalism of Statistical Mechanics with the Variational Multiscale (VMS) method. The MZ-VMS approach leverages both VMS scale-separation projectors as well…

Numerical Analysis · Mathematics 2017-12-29 Eric J. Parish , Karthik Duraisamy

We propose a method for verifying that a given feasible point for a polynomial optimization problem is globally optimal. The approach relies on the Lasserre hierarchy and the result of Lasserre regarding the importance of the convexity of…

Optimization and Control · Mathematics 2021-01-05 Sikun Xu , Ruoyi Ma , Daniel K. Molzahn , Hassan Hijazi , Cédric Josz

Simultaneous Localization and Mapping (SLAM) has wide robotic applications such as autonomous driving and unmanned aerial vehicles. Both computational efficiency and localization accuracy are of great importance towards a good SLAM system.…

Robotics · Computer Science 2022-01-10 Han Wang , Chen Wang , Chun-Lin Chen , Lihua Xie

We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuous- and discrete-time polynomial systems, under semialgebraic set constraints. First,…

Dynamical Systems · Mathematics 2018-07-03 Victor Magron , Marcelo Forets , Didier Henrion

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the…

Optimization and Control · Mathematics 2016-05-03 Zhuo-Xu Cui , Qibin Fan

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…

Optimization and Control · Mathematics 2016-01-20 Marco A. Iglesias

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix…

Signal Processing · Electrical Eng. & Systems 2021-09-21 Yongwei Huang , Sergiy A. Vorobyov , Zhi-Quan Luo

Training foundation models such as ViTs and LLMs requires tremendous computing cost. Low-rank matrix or tensor factorization offers a parameter-efficient alternative, but often downgrades performance due to the restricted parameter space.…

Machine Learning · Computer Science 2025-10-28 Ruijie Zhang , Ziyue Liu , Zhengyang Wang , Zheng Zhang

Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…

Robotics · Computer Science 2016-08-11 Viorela Ila , Lukas Polok , Marek Solony , Pavel Svoboda

We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the…

Optimization and Control · Mathematics 2021-03-05 Felix Kirschner , Etienne de Klerk

In large-scale data processing scenarios, data often arrive in sequential streams generated by complex systems that exhibit drifting distributions and time-varying system parameters. This nonstationarity challenges theoretical analysis, as…

Machine Learning · Computer Science 2026-02-13 Yifei Jin , Xin Zheng , Lei Guo