First-order Constraints Research Articles

On the structure of linear, first-order nonholonomic constraints, and the associated reaction forces

This paper reexamines: (i) the analytical and physical structure of (linear, first-order) nonholonomic constraints and their associated reaction forces, and (ii) the effect of the motion of the frame of reference on the forms of these constraints and forces, in parallel with the constitutive equation theory of continuum mechanics; all the results are expressed in both particle (vectorial) and system forms. The theory clearly shows the precise way in which the acatastatic terms (in the system form of the nonholonomic constraints and in inertial system coordinates) are generated by the motion of the frame of reference relative to inertial space. The general theory is finally applied to the well-known knife-edge/sled problem in a uniformly rotating frame of reference.

On weak continuity and the Hodge decomposition

We address the problem of determining the weakly continuous polynomials for sequences of functions that satisfy general linear first-order differential constraints. We prove that wedge products are weakly continuous when the differential constraints are given by exterior derivatives. This is sufficient for reproducing the Div-Curl Lemma of Murat and Tartar, the null Lagrangians in the calculus of variations and the weakly continuous polynomials for Maxwell’s equations. This result was derived independently by Tartar who stated it in a recent survey article [7]. Our proof is explicit and uses the Hodge decomposition.

On the performance of a contour coding algorithm in the context of image coding part I: Contour segment coding

This paper present an information lossless contour code intended to improve the overall performance of image coding techniques based on segmentation of an image into a set of regions covering the image. This image coding scheme provides individual descriptions for each region composing an image. The boundaries are represented by an information lossless code, while the grey-level evolution associated with pels interior to a boundary is given an approximate description. The algorithm described here provides an efficient code for the boundary of each region by taking advantage of certain first-order constraints related to the segmentation algorithm, the result being an asymptotic decrease in the number of bits per contour point from log 23 (corresponding to the unconstrained 4-connected contour code) to log 2 (1 + √2). An extension of this method treating the case of an entire segmented image as a unit will be presented in a future paper. An interesting result is the existence of a code whose length is bounded by the total number of contour points together with the points that are directly 4-connected to them.

NEWSUMT-A: A General Purpose Program for Constrained Optimization Using Constraint Approximations

The solution of complex constrained optimization problems is often prohibitively expensive because of the computational expense of evaluating the constraints. Under these circumstances the only viable solution is to employ inexpensive constraint approximations accompanied by move-limits that guard against large errors in the approximated constraints. The NEWSUMT-A program is a general purpose optimization program which automates the process of selecting constraint approximations and move-limits to ensure smooth convergence. The present paper describes the theoretical basis and the implementation of the optimization procedure. Examples from the field of structural optimization are presented. These involve stress and displacement constraints which require a costly finite element analysis. Additionally, the performance of two first-order constraint approximations is compared.

Comments on a multiplier condition for problems with state variable inequality constraints

This correspondence points out that a widely quoted necessary condition on the Lagrange multiplier associated with a first-order state variable inequality constraint is not equivalent to Gamkrelidze's multiplier condition. An example is given of a problem for which the latter stronger condition is required to determine optimal trajectories.