Related papers: A generalized power iteration method for solving q…
The generalized orthogonal Procrustes problem (GOPP) plays a fundamental role in several scientific disciplines including statistics, imaging science and computer vision. Despite its tremendous practical importance, it is generally an…
Given multiple point clouds, how to find the rigid transform (rotation, reflection, and shifting) such that these point clouds are well aligned? This problem, known as the generalized orthogonal Procrustes problem (GOPP), has found numerous…
Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA),…
Optimal Power Flow (OPF) can be modeled as a non-convex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method…
A parameterized orthogonality-constrained neural network is proposed for the first time to solve the parameterized generalized inverse eigenvalue problem (PGIEP) on product manifolds, offering a new perspective to address PGIEP. The key…
Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure…
We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…
This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…
In this paper, we consider a class of generalized orthogonal optimization constraint problems (GOOCP) over $\mathbb{R}^{n \times p}$, where the variable $X$ is restricted within the intersection of a certain subspace $\mathcal{F}$ and…
In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition. We establish the weak convergence, global convergence…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
In this paper, a Gauss-Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to a system of linear equations, where the coefficient matrix may be full rank or rank deficient and the system is…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…
Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…
Optimization algorithms play a central role in chemistry since optimization is the computational keystone of most molecular and electronic structure calculations. Herein, we introduce the iterative power algorithm (IPA) for global…