In this paper we study uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. The main tool in our investigation of this question will be a calculus of dual (polar) cones. We give sufficient and in some cases necessary conditions for uniqueness of Lagrange multipliers in general Banach spaces. General results are then applied to two particular examples of the s...

In this paper an optimal control approach for thermal stress reduction inside a Czochralski grown single crystal is presented. Using the lateral heat flux as a control variable, an optimal control formulation for minimizing thermal stress with a given crystal shape is derived. Since thermal stress is also affected by the lateral shape of crystals during growth, the level of the stress can be re...

The Support Vector Machine (SVM) idea has attracted recent attention in solving classiication and regression problems. As an example based method, SVMs distinguish two point classes by nding a separating boundary layer, which is determined by points that become known as Support Vectors (SVs). While the computation of the separating boundary layer is formulated as a linearly constrained Quadrati...

We present a formulation of the FETI substructuring method as a matrix preconditioning algorithm and report on theoretical results and practical experience in large scale parallel implementations. The method has quasi-optimal convergence properties: the condition number can be proved to be independent of the number of subdomains, and to grow at most polylogarithmically with the number of elemen...

Novel architectures such as ResNets have enabled the training of very deep feedforward networks via the introduction of skip-connections, leading to state-of-theart results in many applications. Part of the success of ResNets has been attributed to improvements in the conditioning of the optimization problem (e.g., avoiding vanishing and shattered gradients). In this work we propose a simple me...

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

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

A fast parallel iterative method is proposed for the solution of linear equations arizing from Finite Element discretization of the time harmonic coupled fluid-solid systems in fluid pressure and solid displacement formulation. The fluid and the solid domains are decomposed into nonoverlapping subdomains. Continuity of the solution is enforced by Lagrange multipliers. The system is augmented by...

Interference and collisions greatly limit the throughput of mesh networks that use contention-based MAC protocols such as 802.11. Significantly higher throughput is achievable if transmissions are scheduled. However, traditional methods to compute optimal schedules are computationally intractable (unless co-channel interference is neglected). This paper presents a tractable technique to compute...