Related papers: Implicit Redundancy and Degeneracy in Conic Progra…
We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a…
We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no…
When there are infinitely many scenarios, the current studies of two-stage stochastic programming problems rely on the relatively complete recourse assumption. However, such assumption can be unrealistic for many real-world problems. This…
Qualification conditions (also termed constraint qualifications) help avoid pathological behavior at domain boundaries in convex analysis. By generalizing facial reduction from conic programming to general convex programs of the form $f(x)…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
The first two authors of this paper asserted in Lemma 4 of "New Farkas-type constraint qualifications in convex infinite programming" (DOI: 10.1051/cocv:2007027) that a given reverse convex inequality is consequence of a given convex system…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
We study the problem of removable singularities for degenerate elliptic equations. Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed…
In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of $p$-admissible weights, which may vanish or blow up near the origin. Further, the singularity is allowed to vary…
Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically…
We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs), given by $d$ variables with $n$ inequality constraints. A constraint is called \emph{redundant}, if…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the…
Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
The paper is devoted to the implicit function theorem involving singular mappings.We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to…