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Full-Text Articles in Applied Mathematics
First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang
First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang
LSU Doctoral Dissertations
Nonlinear optimization is a critical branch in applied mathematics and has attracted wide attention due to its popularity in practical applications. In this work, we present two methods which use first-order information to solve two typical classes of nonlinear structured optimization problems.
For a class of unconstrained nonconvex composite optimization problems where the objective is the sum of a smooth but possibly nonconvex function and a convex but possibly nonsmooth function, we propose a unified proximal gradient method with extrapolation, which provides unified treatment to convex and nonconvex problems. The method achieves the best-known convergence rate for first-order methods when …
Finite Element Methods For Elliptic Optimal Control Problems With General Tracking, Seonghee Jeong
Finite Element Methods For Elliptic Optimal Control Problems With General Tracking, Seonghee Jeong
LSU Doctoral Dissertations
This dissertation concerns a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of a domain.
First we explore the elliptic optimal control problem subject to pointwise control constraints. This problem is reduced into a problem that only involves the control. The solution of the reduced problem is characterized by a variational inequality. Then we introduce the elliptic optimal control problem with general tracking and pointwise state constraints. Here we reformulate the optimal control problem into a problem that only involves the state, …