组合与优化哲学博士-连续优化

持续优化是解决从生物分子设计到投资组合管理的现实世界问题的核心数学科学。连续优化意味着找到一个或多个实变量的函数的最小值或最大值
Combinatorics is the study of discrete structures and their properties. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. The PhD involves about two years of grad courses followed by research and a dissertation, and typically lasts four years.<br><br>Continuous optimization is the core mathematical science for real-world problems ranging from design of biomolecules to management of investment portfolios. Continuous optimization means finding the minimum or maximum value of a function of one or many real variables, subject to constraints. The constraints usually take the form of equations or inequalities. Continuous optimization has been the subject of study by mathematicians since Newton, Lagrange and Bernoulli. One major focus of the continuous optimization group at Waterloo is convex optimization, that is, continuous optimization in the case that the objective function and feasible set are both convex. Convex optimization problems have widespread applications in practice and also have special properties that make them amenable to sophisticated analysis and powerful algorithms. Members of the group have carried out fundamental work in convex optimization including new and more efficient algorithms for convex optimization and understanding of the most fundamental properties of convex sets such as properties of the set of positive semidefinite matrices.