This paper addresses the development of the modified adaptive dynamic relaxation (maDR) method. Through a critical review of the merits and disadvantages of previous studies, the primary physical approaches for improving the efficiency of the method are discussed. Emphases are placed on the selection of initial vectors and the calculation of fictitious damping factors. A variety of engineering ...

The structural hierarchy inherent to tensegrities enables a building skin that performs on multiple levels simultaneously. While having one function in the global building mechanics, its individual components can work as self-contained systems balancing tensile and compressive forces locally within them. The behavior of elements under load is linear and thus describable analytically. When these...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

Unit commitment with ramping constraints is a very difficult problem with significant economic impact. A new method is developed in this paper for scheduling units with ramping constraints within Lagrangian relaxation framework based on a novel formulation of the discrete states and the integrated applications of standard dynamic programming for determining the optimal discrete states across ho...

We describe an exact decoding algorithm for syntax-based statistical translation. The approach uses Lagrangian relaxation to decompose the decoding problem into tractable subproblems, thereby avoiding exhaustive dynamic programming. The method recovers exact solutions, with certificates of optimality, on over 97% of test examples; it has comparable speed to state-of-the-art decoders.