Princeton University Press 出版的“鲁棒优化”研究。

简介：
Aharon Ben-Tal, Laurent El Ghaoui, and Arkadi Nemirovski authored this publication, originally copyrighted in 2009 by Princeton University Press. The work is divided into two main sections: Part I, which focuses on Robust Linear Optimization, and Part II, which explores Robust Conic Optimization. Part I commences with a chapter detailing Uncertain Linear Optimization Problems and their corresponding Robust Counterparts. Subsequent chapters delve into the tractability of these robust counterparts and examine non-affine perturbations. Part I continues with an exploration of approximations for scalar chance constraints, followed by investigations into globalized robust counterparts of uncertain linear optimization problems. Illustrative examples are provided, including the synthesis of antenna arrays. Part I concludes with further refinements of safe tractable approximations for scalar chance constraints, incorporating concepts like Bernstein approximation and conditional value at risk. The discussion extends to scenarios beyond independent linear perturbations. Part II initiates with a chapter dedicated to Uncertain Conic Optimization, outlining fundamental concepts and their preliminary considerations. Following this is an analysis of the tractability of robust counterparts for uncertain conic problems, alongside safe tractable approximations of these counterparts derived from uncertain conic inequalities. Part II then presents several solvable cases involving quadratic problems under various uncertainty sets – including scenario uncertainty, interval uncertainty, unstructured norm-bounded uncertainty, and convex quadratic inequalities with unstructured norm-bounded uncertainty – alongside ellipsoidal uncertainty. Finally it illustrates robust linear estimation techniques. The text then transitions to approximating robust counterparts of uncertain conic quadratic problems through structured norm-bounded uncertainty and the case involving ∩-ellipsoidal uncertainty. Subsequently, the work investigates uncertain semidefinite problems containing tractable robust counterparts; examining their inherent properties and tractability alongside relevant exercises. Finally adjustable robust optimization methods are introduced including motivation and counterparts along with affinely adjustable counterparts and synthesis applications for linear controllers culminating in a comprehensive set of exercises and remarks. The concluding Part IV presents selected applications demonstrating the utility of these techniques in areas such as robust linear regression within manufacturing contexts (specifically TV tube production), inventory management utilizing flexible commitment contracts, and the control of multi-echelon multi-period supply chains providing a diverse range of practical examples.