Related papers: Matrix bordering structure of the Faddeev-Jackiw a…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
Continuous-time Bayesian networks (CTBNs) are graphical representations of multi-component continuous-time Markov processes as directed graphs. The edges in the network represent direct influences among components. The joint rate matrix of…
We present an improved construction of the fundamental matrix factorization in the FJRW-theory given in arXiv:1105.2903. The revised construction is coordinate-free and works for a possibly nonabelian finite group of symmetries. One of the…
The general conditions for the applicability of the Faddeev-Jackiw approach to gauge theories are studied. When the constraints are effective a new proof in the Lagrangian framework of the equivalence between this method and the Dirac…
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…
We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics reformulated as the ordinary Maxwell theory with an additional special axion field. In this form, the CFJ model appears as a special case of the pre-metric approach…
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Uniform bounds on sketched inner products of vectors or matrices underpin several important computational and statistical results in machine learning and randomized algorithms, including the Johnson-Lindenstrauss (J-L) lemma, the Restricted…
In this paper, a modified BFGS algorithm is proposed. The modified BFGS matrix estimates a modified Hessian matrix which is a convex combination of an identity matrix for the steepest descent algorithm and a Hessian matrix for the Newton…
By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant $\Lambda$, elegantly encoded in the…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
We introduce a quadratically convergent semismooth Newton method for nonlinear semidefinite programming that eliminates the need for the generalized Jacobian regularity, a common yet stringent requirement in existing approaches. Our…
By unifying various earlier extensions of alternating sign matrices (ASMs), we introduce the notion of prefix-bounded matrices (PBMs). It is shown that the convex hull of these matrices forms the intersection of two special generalized…
In this paper, we provide refined sufficient conditions for the quadratic Chabauty method to produce a finite set of points, with the conditions on the rank of the Jacobian replaced by conditions on the rank of a quotient of the Jacobian…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…
We generalize the notion of Lagrangian subspaces to self-orthogonal subspaces with respect to a (skew-)symmetric form, thus characterizing (skew-)self-adjoint and unitary operators by means of self-ortho-gonal subspaces. By orthogonality…