A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...

This paper provides the explicit expression of investment facing a binding debt ceiling and the explicit expression of the Lagrange multipliers related to the binding debt ceiling constraint. This result allows us to check for misspecification of the parameterizations of these Lagrange multipliers used in Euler investment equations tests during the 1990’s.  2000 Elsevier Science S.A. All right...

The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly dependent equations are also allowed. Both algorithms use the method of Lagrange multipliers to transform the original SLAE into a positively determined functio...

This paper presents a mixed variational framework and numerical examples to treat a bidimensional friction contact problem in large deformation. Two different contact algorithms with friction are developed using the 2D finite element code PLAST2. The first contact algorithm is the classical node-on-segment, and the second one corresponds to an extension of the mortar element method to a unilate...

We consider optimization problems with equality, inequality, and abstract set constraints. We investigate the relations between various characteristics of the constraint set related to the existence of Lagrange multipliers. For problems with no abstract set constraint, the classical condition of quasiregularity provides the connecting link between the most common constraint qualifications and e...

Two linear algebra based strategies are presented to deal with general classical mechanics problems with constraints. Classical concepts such as holonomic and nonholonomic constraints, virtual displacements, principle of virtual work, Hamilton’s principle and method of Lagrange multipliers are critiqued.