Related papers: High-precision linear minimization is no slower th…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence…
In this paper we consider the problem of finding $\epsilon$-approximate stationary points of convex functions that are $p$-times differentiable with $\nu$-H\"{o}lder continuous $p$th derivatives. We present tensor methods with and without…
We present linear prediction as a differentiable padding method. For each channel, a stochastic autoregressive linear model is fitted to the padding input by minimizing its noise terms in the least-squares sense. The padding is formed from…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Algorithms for numerical tasks in finite precision simultaneously seek to minimize the number of floating point operations performed, and also the number of bits of precision required by each floating point operation. This paper presents an…
Computing the convex hull of a planar $n$-point set $P$ is one of the most fundamental problems in computational geometry. It has an $\Omega(n \log n)$ lower bound in the algebraic computation tree model, and many convex hull algorithms…
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…
Let $D$ be the set of $n\times n$ positive semidefinite matrices of trace equal to one, also known as the set of density matrices. We prove two results on the hardness of approximating $D$ with polytopes. First, we show that if $0 <…
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…