Related papers: Lp-Regularized Least Squares (0<p<1) and Critical …
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
Direct methods are widely used for alignment of models to images, due to their accuracy, since they minimize errors in the domain of measurement noise. They have leveraged least squares minimizations, for simple, efficient, variational…
In the minimum constraint removal ($MCR$), there is no feasible path to move from the starting point towards the goal and, the minimum constraints should be removed in order to find a collision-free path. It has been proved that $MCR$…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
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…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…
Convex regression (CR) is an approach for fitting a convex function to a finite number of observations. It arises in various applications from diverse fields such as statistics, operations research, economics, and electrical engineering.…
In the Disjoint Shortest Paths problem one is given a graph $G$ and a set $\mathcal{T}=\{(s_1,t_1),\dots,(s_k,t_k)\}$ of $k$ vertex pairs. The question is whether there exist vertex-disjoint paths $P_1,\dots,P_k$ in $G$ so that each $P_i$…
Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of…
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…
We describe two algorithms to efficiently solve regularized linear least squares systems based on sketching. The algorithms compute preconditioners for $\min \|Ax-b\|^2_2 + \lambda \|x\|^2_2$, where $A\in\mathbb{R}^{m\times n}$ and…
We consider least squares semidefinite programming (LSSDP) where the primal matrix variable must satisfy given linear equality and inequality constraints, and must also lie in the intersection of the cone of symmetric positive semidefinite…
This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…