11:30 AM - 11:55 AM
A Penalty-Free Method with Superlinear Convergence for Equality Constrained Optimization
In this paper, we propose a new penalty-free method for solving nonlinear equality constrained optimization. This method uses different trust regions to cope with the nonlinearity of the objective function and the constraints instead of using a penalty function or a filter. To avoid Maratos effect, we do not make use of the second order correction or the nonmonotone technique, but utilize the value of the Lagrangian function instead of the objective function in the acceptance criterion of the trail step. The feasibility restoration phase is not necessary, which is often used in filter methods or some other penalty-free methods. Global and superlinear convergence are established for the method under standard assumptions. Preliminary numerical results are reported, which demonstrate the usefulness of the proposed method.
11:55 AM - 12:20 PM
Optimal Control for Fracture Propagation Modeled by a Phase-Field Approach
We are concerned with an optimal control problem governed by a fracture model using a phase-field technique. To avoid the non-differentiability due to the irreversibility constraint, the fracture model is relaxed using a penalization approach. Due to the removal of $L^\infty$ bounds on the phase-field, well posedness of the penalized fracture model needs to be analyzed. Existence of a solution to the penalized fracture model is shown and utilized to establish existence of at least one solution for the regularized optimal control problem.
12:20 PM - 12:45 PM
Robust Nonlinear Optimization
Many optimization problems involve uncertain data, or decision variables that cannot be implemented exactly. Problems of this type can be formulated as robust optimization problems. We present an overview of robust nonlinear optimization, and discuss potential algorithmic approaches motivated by standard nonlinear programming approaches.