相关论文: Prox-regular sweeping processes with bounded retra…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…

This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…

The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…

We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…

Let $A$ be an isotropic, sub-gaussian $m \times n$ matrix. We prove that the process $Z_x := \|Ax\|_2 - \sqrt m \|x\|_2$ has sub-gaussian increments. Using this, we show that for any bounded set $T \subseteq \mathbb{R}^n$, the deviation of…

We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of…

Consider linear ill-posed problems governed by the system $A_i x = y_i$ for $i =1, \cdots, p$, where each $A_i$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y_i$. In case $p$ is huge, solving the problem by an…

We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of so--called two--scale methods. We show that this method is…

We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x\inH, the hyperplane through Tx whose normal…

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…

In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in partial differential equations (PDEs) by, e.g., (spatial)…

We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…

In this note we investigate three kinds of applications of the Painlev\'e-Kuratowski convergence of closed sets in analysis that are motivated also by questions from singularity theory. Firstly, we generalise to Lipschitz functions the…

Evolution strategy (ES) is one of the promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on the speed of its convergence is limited on convex quadratic…

Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction…

We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…