Related papers: Rectangular maximum volume and projective volume s…
We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with $n$ vertices. We give exact algorithms that solve these problems in time…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both…
In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
A fast method of an arbitrary high order for approximating volume potentials is proposed, which is effective also in high dimensional cases. Basis functions introduced in the theory of approximate approximations are used. Results of…
We present a software suite for the analysis and optimization of ideal convex polyhedra in hyperbolic 3-space $\mathbb{H}^3$. Using Rivin's variational characterization of ideal polyhedra, we develop efficient algorithms for checking…
An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…