Abstract In this paper, we provide a new insight to the two-phase signal segmentation problem. We propose an augmented Lagrangian variational model based on Chan–Vese’s original one. Using both energy methods and PDE methods, show, in one-dimensional case, that set of minimizers proposed functional contains only binary functions it coincides with This fact allows us obtain two important feature...

Abstract We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling framework for variety of applications. study stationarity regularity concepts, propose flexible augmented Lagrangian scheme. provide theoretical characte...

We consider global convergence properties of the augmented Lagrangian methods on problems with degenerate constraints, with a special emphasis on mathematical programs with complementarity constraints (MPCC). In the general case, we show convergence to stationary points of the problem under an error bound condition for the feasible set (which is weaker than constraint qualifications), assuming ...

Tchebychev iteration may be used for acceleration convergence of an iterative algorithm to solve a general linear system equation. Associating it with the Uzawa method, we suggest a new iterative solution method for the Stokes problems. The new algorithm retains the simplicity and robustness of the Uzawa method. So it requires almost no additional cost of computation, in terms of storage or CPU...

For a given iterate generated by the augmented Lagrangian or the Lagrangian relaxation based method, we derive estimates for the distance to the primal solution of the underlying optimization problem. The estimates are obtained using some recent contributions to the sensitivity theory, under appropriate first or second order sufficient optimality conditions. The given estimates hold in situatio...

This thesis deals with the development of numerical methods for solving nonconvex optimisation problems by means of decomposition and continuation techniques. We first introduce a novel decomposition algorithm based on alternating gradient projections and augmented Lagrangian relaxations. A proof of local convergence is given under standard assumptions. The effect of different stopping criteria...

A novel relaxation labeling (RL) method is presented based on Augmented Lagrangian multipliers and the graded Hoppeld neural network (ALH). In this method, an RL problem is converted into a constrained optimization problem and solved by using the augmented Lagrangian and Hoppeld techniques. The ALH method yields results comparable to the best of the existing RL algorithms in terms of the optimi...