Efficient and robust algorithms for hard, large scale, numerical optimization

我的研究重点是设计和实现高效和健壮的数值算法来解决大规模、困难的优化问题。这些问题出现在许多重要的应用中，例如分子构象、逆成像、机器学习，特别是这些问题出现在困难的组合优化问题的松弛。在许多情况下，这些问题既是大规模的，又是不适定的，即难以数值求解。我使用的技术涉及连续优化、非线性规划，特别是半定规划，SDP。对于SDP，我的研究贡献包括强对偶结果，稳定算法，以及各种应用的松弛研究。对于NLP，我推导了大规模无约束最小化的信赖域算法，以及稳定的序列二次规划方法。

The focus of my research is the design and implementation of efficient and robust numerical algorithms for large scale, hard, optimization problems.  Such problems arise in many important applications, e.g. molecular conformation, inverse imaging, machine learning, and, in particular, these problems arise in the relaxations of hard combinatorial optimization problems. In many instances, these problems are both large scale and ill-posed, i.e. hard to solve numerically.The techniques that I use involve continuous optimization, nonlinear programming, NLP, and in particular, semidefinite programming, SDP.  For SDP, my research contributions include strong duality results, stable algorithms, and the study of relaxations for various applications.  For NLP, I have derived trust region algorithms for large scale unconstrained minimization, as well as stable sequential quadratic programming methods.