It has been shown that the alternating direction method of multipliers (ADMM) is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objective function in the sum of more than two functions without coupled variables. Most recently, we proposed the block-wise ADMM, which was obtained by regrouping the variables and fu...

We present a new approach to a class of non-convex LMI-constrained problem in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with non-convex constraints related to rank conditions. We solve these problems using an extension of the augmented Lagrangian technique. The Lagrangia...

A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and c...

We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and compare different relaxations of them, namely lagrangian relaxation, continuous relaxation, mixed inte...

The estimation of dense depth maps has become a fundamental module in the pipeline of many visual-based navigation and planning systems. The motivation of our work is to achieve fast and accurate in-situ infrastructure modelling from a monocular camera mounted on an autonomous car. Our technical contribution is in the application of a Lagrangian Multipliers based formulation to minimise an ener...

We investigate the augmented Lagrangian dual (ALD) for mixed integer linear programming (MIP) problems. ALD modifies the classical Lagrangian dual by appending a nonlinear penalty function on the violation of the dualized constraints in order to reduce the duality gap. We first provide a primal characterization for ALD for MIPs and prove that ALD is able to asymptotically achieve zero duality g...

Abstract We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The is accomplished by introducing Lagrange multiplier theorem dual program with variables that pointed closed processes. nature assumed the processes essential derivation main results presented in this research...

The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity "Ideal" Ohm's Law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. augmentation combines pointwise vector Lagrange multiplier global penalty function can be used either for iterative enforceme...

This paper presents a coding mode decision algorithm for MPEG-2 spatial transcoding. The optimization for coding mode and quantization scale are formulated in an operational rate distortion sense and solved by Lagarange multiplier method. The experimental results show that the proposed transcoder with optimized coding mode and quantizer can achieve better quality and lower bit rate than those o...