Related papers: Computing real radicals by moment optimization

We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…

We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent…

Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We analyze…

We present an algorithm for computing Groebner bases of vanishing ideals of points that is optimized for the case when the number of points in the associated variety is less than the number of indeterminates. The algorithm first identifies…

We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

We show how the numerical range of a matrix can be used to bound the optimal value of certain optimization problems over real tensor product vectors. Our bound is stronger than the trivial bounds based on eigenvalues, and can be computed…

This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012),…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

In the last decade, the approximate basis computation of vanishing ideals has been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of…

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or…