Related papers: An unconditional lower bound for the active-set me…
We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search…
Active learning allows machine learning models to be trained using fewer labels while retaining similar performance to traditional supervised learning. An active learner selects the most informative data points, requests their labels, and…
In this paper we presented a new driving variable approach in minimum angle rule which is simple and comparatively fast for providing a dual feasible basis. We also present experimental results that compare the speed of the minimum angle…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
We give bounds for the number and the size of the primes $p$ such that a reduction modulo $p$ of a system of multivariate polynomials over the integers with a finite number $T$ of complex zeros, does not have exactly $T$ zeros over the…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
The goal of this paper is to derive new classes of valid convex inequalities for quadratically constrained quadratic programs (QCQPs) through the technique of lifting. Our first main result shows that, for sets described by one bipartite…
In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton…
Let $f \in Q(z)$ be a polynomial or rational function of degree 2. A special case of Morton and Silverman's Dynamical Uniform Boundedness Conjecture states that the number of rational preperiodic points of $f$ is bounded above by an…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
Alon and F\"uredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of the n-dimensional hypercube {0,1}^n except the origin.…
Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
A key property of an algebraic variety is whether it is absolutely irreducible, meaning that it remains irreducible over the algebraic closure of its defining field, and determining absolute irreducibility is important in algebraic geometry…