An improved Lagrangian relaxation (LR) solution to the thermal unit commitment problem (UCP) is proposed in this paper. The algorithm is characterized by: (1) a new Matlab function to determine the optimal path of the dual problem, (2) new initialization procedure of Lagrangian multipliers, based on both unit and time interval classification, (3) a flexible adjustment of Lagrangian multipliers,...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with ramp rate, emission and transmission constraints. The proposed ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian function. In ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty ...

The statistical bundle is the set of couples (Q, W) of a probability density Q and a random 1 variable W such that EQ [W] = 0. On a finite state space, we assume Q to be a probability density with 2 respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is 3 a model for Information Geometry. Velocity and accelleration of a one-dimensional statisti...

Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate variable, and inequality constraints are handled by means of non-negative slack variables that are ...

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...

The natural relativistic generalisation of Landau’s two constituent superfluid theory can be formulated in terms of a Lagrangian L that is given as a function of the entropy current 4-vector sρ and the gradient ∇ρ φ of the superfluid phase scalar. It is shown that in the “cool” regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function L{~s,∇φ} is given ...

We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd–Omojokun class of algorithms,...