A New Derivative-Free Method Using an Improved Under-Determined Quadratic Interpolation Model

Explore a new derivative-free optimization method presented in this 23-minute conference talk from the "One World Optimization Seminar in Vienna" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into an improved under-determined quadratic interpolation model that addresses the Karush-Kuhn-Tucker multiplier's non-determinacy in trust-region iterations. Discover the theoretical motivation, computational details, and implementation-friendly formula derived from Karush-Kuhn-Tucker conditions. Learn how this novel approach selectively treats the last obtained under-determined quadratic model as either quadratic or linear, enhancing existing model-based derivative-free methods. Examine numerical results and released codes that demonstrate the advantages of this groundbreaking quadratic model in derivative-free optimization methods.