Related papers: Lipschitz and H\"older stability of optimization p…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…
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…
A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…
In this work, we consider the inverse problem of simultaneously recovering two classes of quasilinear terms appearing in a parabolic equation from boundary measurements. It is motivated by several industrial and scientific applications,…
Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies…
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a…
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…
In this paper, we mainly study tilt stability and Lipschitz stability of convex optimization problems. Our characterizations are geometric and fully computable in many important cases. As a result, we apply our theory to the group Lasso…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…
We consider equations involving a combination of local and nonlocal degenerate $p$-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and H\"older continuity with an explicit…
In this paper we prove Holder regularity of the gradient for solutions of Dirichlet problem associate to degenerate elliptic equations, extending the recent result of Imbert and Silvestre. Indeed we obtain regularity up to the boundary and…
This paper sheds new light on regularity of multifunctions through various characterizations of directional H\"older /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations,…
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally…