Related papers: Projectional Coderivatives and Calculus Rules
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
Continuous-time projected dynamical systems are an elementary class of discontinuous dynamical systems with trajectories that remain in a feasible domain by means of projecting outward-pointing vector fields. They are essential when…
We investigate the differential calculus defined by Ashtekar and Lewandowski on projective limits of manifolds by means of cylindrical smooth functions and compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more…
Given a compact metric space $X$, the collection of Borel probability measures on $X$ can be made into a compact metric space via the Kantorovich metric. We partially generalize this well known result to projection-valued measures. In…
The aim of this paper is to study geometric properties of non-degenerate smooth projective varieties of small degree from a birational point of view. First, using the positivity property of double point divisors and the adjunction mappings,…
By applying some theorems of Levy and Mordukhovich (Math Program 99: 311--327, 2004) and other related results, we estimate the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one…
It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…
In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
We study the computational expressivity of proof systems with fixed point operators, within the 'proofs-as-programs' paradigm. We start with a calculus muLJ (due to Clairambault) that extends intuitionistic logic by least and greatest…