Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.Includes bibliographical references (leaves 73-75).In this thesis, we use a semidefinite relaxation based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to solve nonconvex Box constrained Quadratic Programming (BoxQP) problems and the comparison of the four methods. For some lower dimensional problems, SDP relaxation methods can achieve tight bounds for the BoxQP problem; whereas for higher dimensional cases (more than 20 dimensions), the bounds achieved by the four Semidefinite programming (SDP) relaxation methods are always loose. To achieve tight bounds for higher dimensional BoxQP problems, we combine the branch-and-bound method and SDP relaxation method to develop an SDP relaxation based branch-and-bound (SDPBB) method. We introduce a sensitivity analysis method for the branching process of SDPBB. This sensitivity analysis method can improve the convergence speed significantly.(cont.) Compared to the interval branch-and-bound method and the global optimization software BARON, SDPBB can achieve better bounds and is also much more efficient. Additionally, we have developed a multisection algorithm for SDPBB and the multisection algorithm has been parallelized using Message Passing Interface (MPI). By parallelizing the program, we can significantly improve the speed of solving higher dimensional BoxQP problems.by Sha Hu.S.M

Branch and Bound algorithms in greenhouse climate control

The horticultural sector has become an increasingly important sector of food production, for which greenhouse climate control plays a vital role in improving its sustainability. One of the methods to control the greenhouse climate is Model Predictive Control, which can be optimized through a branch and bound algorithm. The application of the algorithm in literature is examined and analyzed through small examples, and later extended to greenhouse climate simulation. A comparison is made of various alternative objective functions available in literature. Subsequently, a modidified version of the B&B algorithm is presented, which reduces the number of node evaluations required for optimization. Finally, three alternative algorithms are developed and compared to consider the optimization problem from a discrete to a continuous control space.Grant TIN2015-66680-c2-2-R from the Spanish state in part financed by the European Regional Development Fund (ERDF

Metabolite Mapping with Extended Brain Coverage Using a Fast Multisection MRSI Pulse Sequence and a Multichannel Coil

Multisection magnetic resonance spectroscopic imaging is a widely used pulse sequence that has distinct advantages over other spectroscopic imaging sequences, such as dynamic shimming, large region-of-interest coverage within slices, and rapid data acquisition. It has limitations, however, in the number of slices that can be acquired in realistic scan times and information loss from spacing between slices. In this paper, we synergize the multi-section spectroscopic imaging pulse sequence with multichannel coil technology to overcome these limitations. These combined techniques now permit elimination of the gaps between slices and acquisition of a larger number of slices to realize the whole brain metabolite mapping without incurring the penalties of longer repetition times (and therefore longer acquisition times) or lower signal-to-noise ratios