Related papers: Multiplicative updates for symmetric-cone factoriz…
Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used. Most schemes are based on outer…
Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still…
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We present two conjectures regarding the running time of computing symmetric factorizations for a Hankel matrix $\mathbf{H}$ and its inverse $\mathbf{H}^{-1}$ as $\mathbf{B}\mathbf{B}^*$ under fixed-point arithmetic. If solved, these would…
A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that…
In this work, we generalized and unified two recent completely different works of~\cite{shi2015large} and~\cite{cartis2012adaptive} respectively into one by proposing the cyclic incremental Newton-type gradient descent with cubic…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In…
In submodular $k$-partition, the input is a non-negative submodular function $f$ defined over a finite ground set $V$ (given by an evaluation oracle) along with a positive integer $k$ and the goal is to find a partition of the ground set…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many…
We analyze the scaling matrix, search direction, and neighborhood used in MOSEK's algorithm for nonsymmetric conic optimization [Dahl and Andersen, 2019]. It is proven that these can be used to compute a near-optimal solution to the…
The symmetric rank-one update method is well-known in optimization for its applications in the quasi-Newton algorithm. In particular, Conn, Gould, and Toint proved in 1991 that the matrix sequence resulting from this method approximates the…
Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to construct similarity matrix. However, $k$-NN may mislead clustering since the neighbors…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…