Applications of Functional Interpolation to Optimization

Catalog description

Credits 3. 3 Lecture Hours. Functional interpolation to solve constrained optimization problems; theoretical exploration of mathematical background (least-squares, univariate, multivariate, and neural network basis functions, function projections); univariate functional interpolation: derivation of functionals (by the “η” and the switching-projection formulations) subject to points, derivatives, integrals, linear operators, components, infinite, and nonlinear constraints; multivariate functionals in rectangular domains by tensor and recursive approaches; lower-dimensional constraints; bijective domains mapping; functionals for fractional operators and inequality constraints; applications including ordinary differential equations, partial differential equations, integro-differential equations, homotopy continuation, quadratic and nonlinear programming, indirect optimal control, calculus of variations, geodesic on curved spaces. Prerequisites: Graduate classification or approval of instructor.