This book investigates the critical challenges of determining feasibility and infeasibility within various optimization models. It provides a comprehensive overview of both established and novel algorithms, emphasizing practical applications for linear, nonlinear, and mixed-integer programs, and explores connections to constraint programming.

The book is presented as a timely expository work, aiming to equip practitioners with the knowledge to immediately utilize existing algorithms and software for optimization problems. Its scope is intended to benefit researchers and students across applied sciences by detailing state-of-the-art methods for feasibility and infeasibility in optimization. The content covers a broad range of model forms, including linear, nonlinear, and mixed-integer programs, suggesting a comprehensive resource for those engaged in complex computational tasks. Connections to constraint programming are also highlighted, broadening its applicability.