Optimality conditions and solution methods for some classes of nonconvex and nondifferentiable optimization problems

This dissertation investigates optimality conditions and solution methods for specific classes of nonconvex and nondifferentiable optimization problems. It introduces novel modifications to Zoutendijk's feasible direction method and the Frank–Wolfe algorithm by incorporating the concept of radial epiderivatives in place of classical derivatives. The study begins with a foundational overview of optimization principles, followed by an in-depth exploration of radial epiderivatives, including new theoretical developments and illustrative examples. Subsequent chapters detail the proposed algorithmic modifications and provide rigorous convergence analyses. This work aims to enhance the theoretical framework and practical applications of optimization techniques in complex, nonconvex, and nondifferentiable contexts.