Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we apply a consolidated nons...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...

Abstract In this work we establish the relation between Jacobi last multiplier, which is a geometrical tool in solution of problems mechanics and that provides Lagrangian descriptions constants motion for second-order ordinary differential equations, nonholonomic where dynamics determined by Hamel’s equations.

In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the...