Related papers: A First Order Method for Linear Programming Parame…
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…
Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space.These difficulties can be addressed by second-order approaches that apply a…
A parametric class of trust-region algorithms for unconstrained nonconvex optimization is considered where the value of the objective function is never computed. The class contains a deterministic version of the first-order Adagrad method…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
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…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…