Numerical Methods For Box Constrained Integer Least Squares Problems

Numerical Methods for Box-constrained Integer Least Squares Problems

Numerical Methods for Underdetermined Box-constrained Integer Least Squares Problems

"Integer least squares (ILS) is an important class of optimization problems, which can arise in many applications, such as communications, cryptography and cryptanalysis and global navigation satellite systems. This thesis is concerned with solving the underdetermined box constrained ILS (UBILS) problems. For the two existing algorithms, the direct tree search (DTS) algorithm and the partial regularization (PR) algorithm, we propose to incorporate some lower bounds to speed up the search process. Simulation results show that the proposed lower bounds can make the search process of the DTS algorithm perform more efficiently than the original one. Then we propose a modified DTS algorithm by partially using a best-first search strategy in the search process. Numerical tests results indicate that the new search algorithm is very effective in improving the efficiency of the DTS algorithm with or without incorporating the proposed lower bounds." --

Approximation Methods for Polynomial Optimization

Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.