Minimizers of a class of constrained vectorial variational problems: Part I

2013/10/09 by Hichem Hajaiej, Hajaiej, Hichem, Peter A. Markowich +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #Optimization and Variational Analysis #math.AP #msc:12345 #msc:54321

paper · pdf · doi:10.48550/arxiv.1310.2517

arxiv created 2013/10/09 · arxiv updated 2013/10/10

Abstract

In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our approach hinges on the concentration-compactness approach. In the second part, we will treat orthogonal constrained problems for another class of integrands using density matrices method.

Related

• Existence of minimizers of functionals involving the fractional gradient\n in the abscence of compactness, symmetry and monotonicity
• Variational problems on product spaces Different obstacle constraints
• A weak-strong convergence property and symmetry of minimizers of constrained variational problems in ℝ^N
• Variational analysis in normed Spaces with applications to constrained optimization
• Analysis of local minima for constrained minimization problems