Lagrange Multiplier Expression Methods for Optimization

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Optimization techniques are useful for solving problems in economics, telecommunications, quantum physics, and other fields. This project involves Lagrange multiplier expression methods for optimization, which are use useful in computing. The project identifies and aims to solve various research tasks from the field of optimization within computational mathematics and related areas. The research topics of this project have broad applications in many areas of STEM. The computational methodology produced by this project will be highly useful in applications such as game theory, power allocation, environment pollution control, quantum entanglement, and tensor optimization. This project will also involve training and education for young scholars.This project aims to solve various research problems in optimization relevant for the applications. Specifically, the project will involve Lagrange multiplier expressions which provide useful framework within computational mathematics. Expressing Lagrange multipliers in terms of objective and constraining functions is an important issue in optimization. Tight convex relaxation is efficient for solving computational questions. The research topics include polynomial optimization, convex algebraic geometry, moment and tensor problems, bilevel optimization, generalized Nash equilibrium problems, stochastic optimization, tensor computation, tensor optimization, and other related problems. The project will address computational questions involving polynomials, matrices, moments and tensors, frequently appearing from various applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.