We consider the problem of minimizing the $L^\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$ norm of a function of the gradient and the map itself. We assume zeroth and first order Dirichlet boundary data, corresponding to the “hinged” and the “clamped” cases. By employing the method of $L^p$ approximations, we establish the existence of a special $L^\infty$ minimizer, which solves a divergence PDE system with measure coefficients as parameters. This is a counterpart of the Aronsson-Euler system corresponding to this constrained variational problem. Furthermore, we establish upper and lower bounds for the eigenvalue.

Supply chains are fundamental to the economy of the world and many supply chains focus on perishable items, such as food, or even clothing that is subject to a limited shelf life due to fashion and seasonable effects. G-networks have not been previously applied to this important area. Thus in this paper, we apply G-networks to supply chain systems and investigate an optimal order allocation problem for a N-node supply chain with perishable products that share the same order source of fresh products. The objective is to find an optimal order allocation strategy to minimize the purchase price per object from the perspective of the customers. An analytical solution based on G-networks with batch removal, together with optimization methods are shown to produce the desired results. The results are illustrated by a numerical example with realistic parameters.

A new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply, and complete asset markets. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in infinite-dimensional spaces and their representation as a summable sequence and a direct application of the inward-boundary fixed point theorem.

We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. Themembrane is characterized by its Canham-Helfrich energy (Willmore energy with areaconstraint) and acts as a boundary force on the Navier-Stokes system modeling anincompressible fluid. We give a concise description of the model and of the associatednumerical scheme. We provide numerical simulations with emphasis on the comparisonsbetween different types of flow: the geometric model which does not take into account thebulk fluid and the biomembrane model for two different regimes of parameters.

Optimal control problems for semilinear elliptic equationswith control constraints and pointwise state constraints arestudied. Several theoretical results are derived, which arenecessary to carry out a numerical analysis for this class ofcontrol problems. In particular, sufficient second-order optimalityconditions, some new regularity results on optimal controls and asufficient condition for the uniqueness of the Lagrange multiplierassociated with the state constraints are presented.

We consider a multiobjective optimization problem with a feasible setdefined by inequality and equality constraints such that all functionsare, at least, Dini differentiable (in some cases, Hadamard differentiableand sometimes, quasiconvex). Several constraint qualifications are givenin such a way that generalize both the qualifications introduced by Maedaand the classical ones, when the functions are differentiable. Therelationships between them are analyzed. Finally, we give severalKuhn-Tucker type necessary conditions for a point to be Pareto minimumunder the weaker constraint qualifications here proposed.

We consider a general loaded arch problem with a small thickness. Toapproximate the solution of this problem, a conforming mixed finite elementmethod which takes into account an approximation of the middle line of thearch is given. But for a very small thickness such a method gives poor errorbounds. the conforming Galerkin method is then enriched with residual-freebubble functions.

The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of controltheory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-stateinequality constraints. We show how to obtain Lagrange multipliers in Lp spaces for linear problems and give an application to linearparabolic optimal control problems.

For a sequence of random variables {Xn, n ≧ 0}, optimal stopping is considered over stopping times T constrained so that ET ≦ α, for some fixed α > 0. It is shown that under certain circumstances a Lagrangian approach may be used to reduce the problem to an unconstrained optimal stopping problem of a conventional type. The optimal value of the natural dual problem is shown to be equal to the optimal value of the original (primal) problem when certain randomised stopping times are permitted. Two examples are considered in detail.

This paper presents characterizations of optimality for the abstract convex program

when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.