SC Seminar: Long Chen

Dr. Long Chen, Chair for Scientific Computing (SciComp), TU Kaiserslautern

A Gradient Descent Akin Method for Constrained Optimization


Motivated by the applications of large-scale shape optimization problems and inspired by singular value decomposition, we present a “gradient descent akin method” (GDAM) for solving constrained optimization problems. At each iteration, we compute a search direction using a linear combination of the negative and normalized objective and constraint gradient by introducing a parameter \zeta. While the principled idea behind GDAM is similar to that of gradient descent, we show its connection to the classical logarithmic barrier interior-point method and argue that it can be considered a first-order interior-point method. The convergence behavior of the method is studied using a dynamical systems approach. In particular, we show that the continuous-time optimization trajectory finds local solutions by asymptotically converging to the central path(s) of the barrier interior-point method. Furthermore, we show that the convergence rate of the method is bounded relative to \zeta. Numerical examples are reported, which include both common test examples and real-world applications in shape optimization. Finally, we show recent progress in the practical implementation of GDAM by incorporating Nesterov’s Acceleration Gradient method.

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