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This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form $QAP(A,B)$, by showing that the identity permutation is optimal when $A$ and $B$ are respectively a Robinson similarity and…
Efficiently optimizing Nondeterministic Polynomial time (NP) problems in polynomial time has profound implications in many domains. CMOS oscillator networks have been shown to be effective and efficient in approximating certain NP-hard…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
We examine possibility to design an efficient solving algorithm for problems of the class \np. It is introduced a classification of \np problems by the property that a partial solution of size $k$ can be extended into a partial solution of…
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
Recent results in the theory and application of Newton-Puiseux expansions, i.e. fractional power series solutions of equations, suggest further developments within a more abstract algebraic-geometric framework, involving in particular the…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…
In this paper, we study some anisotropic singular perturbations for a class of linear elliptic problems. We show a global asymptotic expansion of the solution in certain functional space.
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving…
We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some of the approaches to the general area and…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…