Related papers: Analysis of local minima for constrained minimizat…
We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
In this paper we present necessary and sufficient conditions (in terms of {\L}ojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which…
We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density)…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore. Our result involves fine a priori estimates of the moving boundary evolution, Banach…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable…
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…
We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…
We consider vector and set optimization problems with respect to variable domination structures given by set-valued mappings acting between the preimage space and the image space of the objective mapping, as well as by set-valued mappings…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
This paper studies a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which depends on an artificial potential function used to avoid…
We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…
In this work, we investigate the variational problem $$\rho_x^\ast = \text{argmin}_{\rho_x} D(G\#\rho_x, \rho_y)\,, $$ where $D$ quantifies the difference between two probability measures, and ${G}$ is a forward operator that maps a…
In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a…