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...

We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary...

Efficiency multipliers for construction productivity are often estimated on an ad-hoc basis, depending on the project characteristics. The purpose of the study is to define a structured approach allowing the determination of the appropriate empirical productivity relations and efficiency multipliers along with their respective values. The proposed method breaks down a given construction activit...

The heart of the MAC unit is the multiplier. Multipliers are the fundamental components in all digital processing systems. Many research efforts have been devoted to reducing the power dissipation of different multipliers. The largest contribution to the power consumption in a multiplier is due to generation and reduction of partial products. Among multipliers, tree multipliers are used in high...