In this paper, we give a comparison between some notions of weak sharp minima introduced in [5,15,43] for set-valued optimization problems. Besides, establish Lagrange multiplier rules general constrained problems involving new scalarization functionals based on the oriented distance. Moreover, provide sufficient optimality conditions considered without any convexity assumptions.

This paper presents a unified approach to solve different bilinear factorization problems in Computer Vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization problem where one of the factors is constrained to lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem. Thi...

The primal hybrid method for solving second-order elliptic equations is extended from finite element approximations to general bases. Variational techniques are used to show convergence of approximations to the solution of the homogeneous Dirichlet problem for selfadjoint equations. Error estimates are obtained and examples are given. Introduction Lagrange multipliers have been employed to defi...

We discuss Lagrange multiplier rules from a variational perspective. This allows us to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.

These notes were developed for the needs of the 6.291 class at M.I.T. (Spring 2001). They are copyright-protected, but they may be reproduced freely for noncommercial purposes.

Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers

are called stationary Stokes equations, where u : Ω→ R denotes the velocity of the uid, p : Ω→ R denotes the pressure and f : Ω → R is the density of forces acting on the uid (e.g. gravitational force). The Stokes equations govern a ow of a steady, viscous, incompresible uid. We note that (1) is called the momentum equation and (2) is called the incompressibility equation. We supplement the sys...