Constrained optimal control can be remarkably challenging to control. In this paper, optimization based approach for constrained optimal control of the integrating process is investigated through inventory control from using of the PI controller in the servo problem. The Lagrangian multiplier method is applied to find the PI parameters by solving the constrained optimal problem. The developed m...

Consider a large mixed integer linear problem where structure of the constraint matrix is sparse, with independent blocks, and coupling constraints and variables. There is one of the groups of constraints to make difficult the application of Benders scheme decomposition. In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we pre...

This handout presents the second derivative test for a local extrema of a Lagrange multiplier problem. The Section 1 presents a geometric motivation for the criterion involving the second derivatives of both the function f and the constraint function g. The main result is given in section 3, with the special cases of one constraint given in Sections 4 and 5 for two and three dimensions respecti...

The matching velocity problem for the steady-state Navier-Stokes system is considered. We introduce an extended domain method for solving optimal boundary control problems. The Lagrangian multiplier method is applied to the extended domain with distributed controls and used to determine the optimality system and the control over the boundary of the inner domain. The existence, the differentiabi...

A constrained optimization method, called the Lagrange-Hoppeld (LH) method, is presented for solving Markov random eld (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian mul-tiplier technique with the Hoppeld network to solve a constrained optimization problem into which the original Bayesian estimation problem is reform...

An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a Hamiltonian for a degenerate Lagrangian is just that of solving a corresponding Clairaut equation with a subsequent application of the proposed Legendre-Clairau...

We propose a new version of the superfield action for a closed D = 10, N = 1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called ’Wess-Zumino part’ of ...

We establish local convergence and rate of convergence of the classical augmented Lagrangian algorithm under the sole assumption that the dual starting point is close to a multiplier satisfying the second-order sufficient optimality condition. In particular, no constraint qualifications of any kind are needed. Previous literature on the subject required, in addition, the linear independence con...

A covariant Lagrangian formulation of a solution to the cosmological constant problem, based on vizualising the fluctuations of the vacuum energy as a nonequilibrium process with stochastic behaviour, is presented. The variational principle yields equations of motion for the cosmological “constant” Λ, treated as a dynamical field, together with an equation for a Lagrange multiplier field φ, and...

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest solve among all economic mechanisms. In this paper, we develop computationally efficient iterative mechanisms for clearing combinatorial exchanges. The mechani...