In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...

Many optimization models of neural networks need constraints to restrict the space of outputs to a subspace which satisfies external criteria. Optimizations using energy methods yield "forces" which act upon the state of the neural network. The penalty method, in which quadratic energy constraints are added to an existing optimization energy, has become popular recently, but is not guaranteed t...

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

Post-Optimum Sensitivity Analysis (POSA) extends numerical design optimization to provide additional information on how the and performance would change if various parameters constraints were varied. POSA is challenging since it typically requires accurate gradients gradient-based problems that Lagrange multipliers. To overcome this problem, paper introduces a technique automatically tune with ...

A quadratic programming problem with positive definite Hessian and bound constraints is solved, using a Lagrange multiplier approach. The proposed method falls in the category of exterior point, active set techniques. An iteration of our algorithm modifies both the minimization parameters in the primal space and the Lagrange multipliers in the dual space. Comparative results of numerical experi...

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives ...

We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.

A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. We discuss in this paper augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discu...

Space-time finite element methods for dynamic frictional contact problems are discussed in this article. The discretization scheme is based on a mixed formulation of the continuous problem, where the Lagrange multipliers represent the contact and frictional stresses. Using piecewise d-linear and globally continuous basis functions in space and time to construct the trial space for the displacem...

We studied a class of Service Overlay Network (SON) capacity allocation problem with Grade of Service (GoS) constraints. Similar problems in the literature are typically formulated as either a Maximum Profit (MP) optimization problem or a Minimum Cost (MC) optimization problem. In this article we investigate the relationship between the MP and MC formulations. When the service charges are zero,...