A nite element formulation to deal with the friction contact problem between an elastic body and a rigid foundation is presented. An augmented Lagrangian method, which incorporates two Lagrange multipliers and a slack variable in the constraint equation, is developed. In this method, the solution is achieved through a Newton-Raphson monolithic iterative strategy and leads to simple implementati...

We introduce and study the primal-dual exterior point (PDEP) method for convex optimization problems. The PDEP is based on the Nonlinear Rescaling (NR) multipliers method with dynamic scaling parameters update. The NR method at each step alternates finding the unconstrained minimizer of the Lagrangian for the equivalent problem with both Lagrange multipliers and scaling parameters vectors updat...

The paper analyzes dynamic problems of stochastic optimization in discrete time. The problems under consideration are concerned with maximizing concave functionals on convex sets of feasible strategies (programs). Feasibility is defined in terms of linear inequality constraints in L∞ holding almost surely. The focus of the work is the existence of dual variables – stochastic Lagrange multiplier...

The paper deals with a general optimal control problem for age-structured systems. A necessary optimality condition of Pontryagin type is obtained, where the novelty is in that mixed control-state constraints are present. The proof uses an abstract Lagrange multiplier theorem, and the main difficulty is to obtain regularity of the Lagrange multipliers in the particular problem at hand.

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

A class of optimal control problems for semilinear elliptic equations with mixed control-state constraints is considered. The existence of bounded and measurable Lagrange multipliers is proven. As a particular application, the Lavrentiev type regularization of pointwise state constraints is discussed. Here, the existence of associated regular multipliers is shown, too.

The Variational Iteration Method (VIM) is an iterative method that approximates solutions of differential equations. The method is a modification of the so-called general Lagrange multipliers [2]. The method is based on the idea of constructing a correction functional that uses a Lagrange multiplier. In this study, we analyse some basic properties of the Lagrange multiplier; and using these, we...

A parallel nonoverlapping subdomain Schwarz alternating algorithm with Lagrange multipliers and interface relaxation is proposed for linear elliptic interface problems with discontinuities in the solution, its derivatives, and the coefficients. New features of the algorithm include that Lagrange multipliers are introduced on the interface and that it is used to solve equations with discontinuou...

Lagrange multipliers are central to analytical and computational studies in linear and nonlinear optimization and have applications in a wide variety of fields, including communication, networking, economics, and manufacturing. In the past, the main research in Lagrange multiplier theory has focused on developing general and easily verifiable conditions on the constraint set, called constraint ...

We minimize elastic energies on framed curves which penalize both curvature and torsion. also discuss critical points using the infinite dimensional version of Lagrange multipliers' method. Finally, some examples arising from applications are discussed numerical experiments presented.