Ioannis C. Demetriou and Panos M. Pardalos (eds): Approximation and Optimization: Algorithms, Complexity and Applications

Oleg Burdakov
2020 SN Operations Research Forum  
The collection of individual papers is a mix of state of the art research articles on Approximation and Optimization, surveys of new work, and relevant applications in science, engineering, and social sciences. The book consists of eleven chapters. A brief survey to the papers is presented in the first chapter. A short review of the later chapters is given in the following paragraphs. The second chapter ("Evaluation Complexity Bounds for Smooth Constrained Nonlinear Optimization using Scaled
more » ... Conditions and High-order Models" by C. Cartis, N.I.M. Gould, and P.L. Toint) considers evaluation complexity for solving constrained optimization. This paper presents theoretical results on a subject where the authors have made important contributions. It starts by considering the case with convex constraints and shows that the complexity bound of O( −3/2 ) derived from previous work of the authors for computing an -approximate firstorder critical point can be obtained under significantly weaker assumptions. This result is generalized to the case where pth-order derivatives are available resulting in a bound of O( −(p+1)/p ) evaluations. It is also shown that the bound of
doi:10.1007/s43069-020-0006-9 fatcat:wqennjmsr5csxlpfpbhhxrx4ju