Commercial finite element software follow cautiously the numerical methods developed by scientific community. Even though phase-field method is not a default option in Abaqus, code proposes unique way to implement and test complex, extraneous models. In last five years, fracture models Abaqus have gained unbelievable popularity among scientists engineers alike. However, most implementations are...

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

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...

The hybridization technique is applied to replace the macro-hybrid mixed finite element problem for the diffusion equation by the equivalent cell-based formulation. The underlying algebraic system is condensed by eliminating the degrees of freedom which represent the interface flux and cell pressure variables to the system containing the Lagrange multipliers variables. An approach to the numeri...

In this paper, we consider variational iteration method (VIM) to obtain exact solution to the Fisher’s equation. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is possible to find the exact solution or an approximate solution of the problem.

‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...

In solving certain optimization problems, the corresponding Lagrangian dual problem is sometimes solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which suggests that for all optimization problems the optimal dual function value is smaller than or equal to...

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multiplie...

We regard a network of systems with coupled dynamics or constraints that we want to control optimally. The cost function is assumed to be separable and convex. We show that the corresponding centralized model predictive control (MPC) problem can be recast as a separable convex optimization problem. Furthermore, we present a dual-based decomposition method, called here the proximal center method...

It is known that when the set of Lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton, this set may contain so-called critical multipliers. This special subset of Lagrange multipliers defines, to a great extent, stability pattern of the solution in question subject to parametric perturbations. Criticality of a Lagrange multiplier can b...