This paper examines the bit and power allocation problem for orthogonal frequency division multiplexing systems in which the overall transmission power is minimized by constraining the fixed data rate and bit error rate. To provide the optimal allocation with less computational complexity, we propose new bit and power allocation schemes based on the Lagrangian method. Firstly, we propose an ini...

This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

In this paper, for nonconvex optimization problem with both equality and inequality constrains, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. The global convergence is established without requiring the boundedness of multiplier sequences. In particular, if the algorithm terminates in finite steps, then we obtain a KKT point of the primal pr...

This paper describes a new approach to Fixed rate Entropy coded Vector Quanti zation FEVQ for stationary memoryless sources where the structure of code words are derived from a variable length scalar quantizer We formulate the quantization search operation as a zero one integer optimization problem and show that the resulting integer program can be closely approximated by solving a simple linea...

We propose an optimal quadtree (QT)-based motion estimator for video compression. It is optimal in the sense that for a given bit budget for encoding the displacement vector field (DVF) and the QT segmentation, the scheme finds a DVF and a QT segmentation which minimizes the energy of the resulting displaced frame difference (DFD). We find the optimal QT decomposition and the optimal DVF jointl...

The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by        ...

Although the Lagrangian method is a powerful dual search approach in integer programming, it often fails to identify an optimal solution of the primal problem. The p-th power Lagrangian method developed in this paper ooers a success guarantee for the dual search in generating an optimal solution of the primal integer programming problem in an equivalent setting via two key transformations. One ...