Related papers: Generic continuity of the perturbed minima of cert…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…

Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…

Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is…

We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…

We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…

In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…

We consider a special form of parametric generalized equations arising from electronic circuits with AC sources and study the effect of perturbing the input signal on solution trajectories. Using methods of variational analysis and strong…

We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by…

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…

The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…

The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…

A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…

The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…

A well known result states that stability criterion for matchings in two-sided markets doesn't ensure uniqueness. This opens the door for a moral question with regard to the optimal stable matching from a social point of view. Here, a new…

In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…