Related papers: The self-concordant perceptron is efficient on a s…
It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically…
In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…
This paper presents a novel online learning method that aims at finding a separator hyperplane between data points labelled as either positive or negative. Since weights and biases of artificial neurons can directly be related to…
Binary linear classification has been explored since the very early days of the machine learning literature. Perhaps the most classical algorithm is the Perceptron, where a weight vector used to classify examples is maintained, and additive…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…
A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. The algorithm also overcomes the core…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…