Related papers: Efficient parallel optimization for approximating …
In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $\epsilon$, our algorithm achieves a $1/e -…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We study the $k$-median clustering problem for high-dimensional polygonal curves with finite but unbounded number of vertices. We tackle the computational issue that arises from the high number of dimensions by defining a…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
The use of Model Predictive Control in industry is steadily increasing as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively…
This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…
One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…