Neculai Andrei Bücher

Focusing on a novel derivative-free optimization method, this book introduces an algorithm that utilizes randomly generated trial points within defined domains. At each iteration, the best points are selected based on various rules, setting it apart from traditional methods. The approach demonstrates effectiveness in tackling a wide range of unconstrained optimization problems, particularly those with high variable counts, as evidenced by extensive numerical experiments involving 140 problems with up to 500 variables, showcasing its efficiency and robustness.

The book delves into the nonlinear behavior of thin-wall shells, both single and multilayered, particularly in the presence of delamination areas. It employs a numerical approach to investigate how these structures respond to different uniform and non-uniform loadings. Key aspects include the analysis of branching points and the construction of bifurcation paths, providing valuable insights into the stability and performance of these engineering materials under various conditions.

The book explores two distinct methodologies for problem-solving, delving into their theoretical foundations and practical applications. It emphasizes critical thinking and analytical skills, guiding readers through step-by-step processes for each approach. The author provides real-world examples and case studies to illustrate how these methods can be effectively utilized in various scenarios. By integrating these techniques, readers can enhance their decision-making abilities and tackle complex challenges with confidence.

Focusing on the theoretical and computational aspects of algorithms for continuous nonlinear optimization, this book is designed for scientists and graduate students in fields like mathematical programming and operations research. It provides insights into using GAMS technology, equipping readers with the knowledge to model and solve complex, large-scale optimization problems. With a foundation in nonlinear optimization and linear algebra, readers will learn to harness GAMS's capabilities effectively for their applications in various industries.

The book offers an in-depth theoretical and computational exploration of both unconstrained and constrained optimization algorithms, highlighting the integration of advanced computational linear algebra techniques. It provides a rigorous yet accessible discussion on the convergence properties of nonlinear optimization methods, equipping readers with the knowledge to validate their own algorithms. Additionally, it examines the performance of various modern algorithms across diverse test problems and real-world applications, making it a valuable resource for understanding complex optimization challenges.