Department of Mathematics Sathyabama University, Chennai – 119 [email protected] Abstract This paper deals with the Distributed Generation (DG) capacity of the electrical power system. DG capacity is formulated as a Mixed Integer Programming (MIP) problem with respect to various operating constraints in power generation. The objective of this model is to minimize the real power loss by ...

Abstract. The augmented Lagrangian method is an attractive approach for solving linearly constrained convex optimization problems (CCOP). The method is iterative and the task in each iteration is to solve a (convex optimization) sub-problem whose dimension is equal to the number of variables. For large problems, solving such a sub-problem can be still very expensive. In this paper, we propose a...

A class of `1-regularized optimization problems with orthogonality constraints has been used to model various applications arising from physics and information sciences, e.g., compressed modes for variational problems. Such optimization problems are difficult to solve due to the non-smooth objective function and nonconvex constraints. Existing methods either are not applicable to such problems,...

We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple upd...

We consider the problem of tracking a benchmark target portfolio of financial securities in particular the S&P 500. Linear integer programming models are developed that seeks to track a target portfolio using a strict subset of securities from the benchmark portfolio. The models represent a clustering approach to select securities and also include additional constraints that aim to control risk...

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a mi...

In this paper, a hybrid Lagrangian–Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles fixed set of Eulerian quadrature points. This transfer based on smooth radial kernel involved in compliance objective avoid artificial checkerboard ...

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincaré equations in a new fashion and we show...

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution acros...