Related papers: On Metric Subregularity for Convex Constraint Syst…
This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality…
In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and…
This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
We consider a generalization of the hyperplane problem to arbitrary measures in place of volume and to sections of lower dimensions. We prove this generalization for unconditional convex bodies and for duals of bodies with bounded volume…
We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed…
This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order…
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it…
Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint qualification, which includes Mangasarian-Fromovitz constraint…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…
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…
Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however, extensions are more challenging. Nonetheless, in…
Nonconvex optimal-control problems governed by evolution problems in infinite-dimensional spaces (as e.g. parabolic boundary-value problems) needs a continuous (and possibly also smooth) extension on some (preferably convex)…
We develop a numerical method for the computation of a minimal convex and compact set, $\mathcal{B}\subset\mathbb{R}^N$, in the sense of mean width. This minimisation is constrained by the requirement that $\max_{b\in\mathcal{B}}\langle b ,…
In this paper, in the setting of Hilbert spaces, we consider a Tikhonov regularized second-order plus first-order primal-dual dynamical system with asymptotically vanishing damping for a linear equality constrained convex optimization…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…