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This paper deals with a stowage plan for containers in a container ship. Since the approach to the containers on board the ship is only from above, it is often the case that containers have to be shifted. Shifting is deÿned as the temporary removal from and placement back of containers onto a stack of containers. Our aim is to ÿnd a stowage plan that(More)
Partial differential equations are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis. Additional features of this new edition include broader coverage of PDE methods and(More)
This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of random variables is widespread. We introduce algorithms to nd upper bounds on the optimal value of two-stage and multi-stage stochastic(More)
Opti-Money is a decision-support system for allocating assets that was developed at Bank Hapoalim, Israel's largest bank. Based on customer-and market-specific inputs, we solve a modified Markowitz-type nonlinear programming problem to produce optimal tailor-made investment portfolios in terms of asset classes. In its five years of operation, this mature(More)
A generally nonconvex optimization problem with equality constraints is studied. The problem is introduced as an " inf sup " of a generalized augmented Lagrangian function. A dual problem is defined as the " sup inf' of the same generalized augmented Lagrangian. Sufftcient conditions are derived for constructing the augmented Lagrangian function such that(More)