Related papers: Projection and rescaling algorithm for finding max…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
In this monograph, we review and develop variable projection Gauss-Newton, Levenberg-Marquardt and Newton methods for the Weighted Low-Rank Approximation (WLRA) problem, which has now an increasing number of applications in many scientific…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
We propose a new algorithm for approximating the metric projection onto a superelliptic disk of order $p>1$, i.e., the convex hull of a superellipse (Lam\'e curve), and prove its convergence.
We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP)…
Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
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…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
We consider lift-and-project methods for combinatorial optimization problems and focus mostly on those lift-and-project methods which generate polyhedral relaxations of the convex hull of integer solutions. We introduce many new variants of…
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…
We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…
The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau's…
The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…