English
Related papers

Related papers: Stability Analysis for Composite Optimization Prob…

200 papers

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

Analysis of PDEs · Mathematics 2018-08-06 Jeremy LeCrone , Gieri Simonett

Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…

Analysis of PDEs · Mathematics 2016-04-26 Björn Augner , Birgit Jacob

We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…

Classical Analysis and ODEs · Mathematics 2017-04-12 Richard Gratwick

Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…

Optimization and Control · Mathematics 2017-06-12 Vu Van Dong

We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…

Optimization and Control · Mathematics 2022-07-06 Stephan Eckstein , Marcel Nutz

This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…

Optimization and Control · Mathematics 2014-09-29 Ian R. Manchester , Jean-Jacques E. Slotine

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…

Systems and Control · Electrical Eng. & Systems 2019-11-04 Yohei Hosoe , Tomomichi Hagiwara

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…

Analysis of PDEs · Mathematics 2020-02-13 Fabrício Cristófani , Ademir Pastor

We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…

Numerical Analysis · Mathematics 2023-04-25 Erik Burman , Janosch Preuss

In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…

Classical Analysis and ODEs · Mathematics 2021-06-02 Benoît Kloeckner

We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…

Optimization and Control · Mathematics 2018-07-25 Marc Dambrine , Jimmy Lamboley , M Dambrine-J

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…

Classical Analysis and ODEs · Mathematics 2010-09-16 Antonio Canada , Salvador Villegas

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…

Optimization and Control · Mathematics 2009-03-03 John M. Davis , Ian A. Gravagne , Billy J. Jackson , Robert J. Marks

In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…

Optimization and Control · Mathematics 2024-08-27 Assalé Adjé

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Optimization and Control · Mathematics 2020-09-04 Daniel Reem , Simeon Reich , Alvaro De Pierro

We develop a general theory for linear stability of traveling waves of second order in time PDE's. More precisely, we introduce an explicitly computable index $\om^*\in (0, \infty]$ (depending on the self-adjoint part of the linearized…

Analysis of PDEs · Mathematics 2015-05-30 Milena Stanislavova , Atanas Stefanov

Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…

Optimization and Control · Mathematics 2018-08-16 Ying Cui , Tsung-Hui Chang , Mingyi Hong , Jong-Shi Pang

In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…

Optimization and Control · Mathematics 2024-10-25 Boushra Abbas

The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…

Optimization and Control · Mathematics 2020-06-17 Ashkan Mohammadi , Boris S. Mordukhovich , M. Ebrahim Sarabi

In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…

Analysis of PDEs · Mathematics 2022-10-27 Marcel Dengler