The book "Nonlinear Multiobjective Optimization" by Kaisa Miettinen is part of the International Series in Operations Research & Management Science. It provides a comprehensive survey and review of the literature and state-of-the-art in nonlinear (deterministic) multiobjective optimization. The book is divided into three parts: Terminology and Theory, Methods, and Related Issues. **Part I: Terminology and Theory** - **Introduction**: Discusses the problem setting, general notation, and background concepts. - **Concepts**: Explains Pareto optimality, decision makers, ranges of the Pareto optimal set, weak Pareto optimality, value function, efficiency, trade-offs, marginal rate of substitution, proper Pareto optimality, and Pareto optimality tests. - **Theoretical Background**: Covers differentiable and nondifferentiable optimality conditions, sensitivity analysis, and duality. **Part II: Methods** - **No-Preference Methods**: Introduces the global criterion method and the multiobjective proximal bundle method. - **A Posteriori Methods**: Describes the weighting method, ε-constraint method, hybrid method, method of weighted metrics, achievement scalarizing function approach, and other a posteriori methods. - **A Priori Methods**: Explores the value function method, lexicographic ordering, and goal programming. - **Interactive Methods**: Details various interactive methods such as the surrogate worth trade-off method, Geoffrion-Dyer-Feinberg method, sequential proxy optimization technique, Tchebycheff method, step method, reference point method, GUESS method, satisficing trade-off method, light beam search, reference direction approach, and NIMBUS method. **Part III: Related Issues** - **Comparing Methods**: Provides a comparative table of interactive methods and discusses method selection tools. - **Software**: Reviews available software for multiobjective optimization. - **Graphical Illustration**: Discusses methods for illustrating the Pareto optimal set and sets of alternatives. - **Future Directions**: Offers insights into future research directions. - **Epilogue**: Concludes the book with reflections on the field. The book aims to provide a consistent and up-to-date survey of nonlinear multiobjective optimization, suitable for researchers, students, and professionals in various fields. It includes a detailed bibliography and theoretical background, making it a valuable resource for both beginners and advanced readers.The book "Nonlinear Multiobjective Optimization" by Kaisa Miettinen is part of the International Series in Operations Research & Management Science. It provides a comprehensive survey and review of the literature and state-of-the-art in nonlinear (deterministic) multiobjective optimization. The book is divided into three parts: Terminology and Theory, Methods, and Related Issues. **Part I: Terminology and Theory** - **Introduction**: Discusses the problem setting, general notation, and background concepts. - **Concepts**: Explains Pareto optimality, decision makers, ranges of the Pareto optimal set, weak Pareto optimality, value function, efficiency, trade-offs, marginal rate of substitution, proper Pareto optimality, and Pareto optimality tests. - **Theoretical Background**: Covers differentiable and nondifferentiable optimality conditions, sensitivity analysis, and duality. **Part II: Methods** - **No-Preference Methods**: Introduces the global criterion method and the multiobjective proximal bundle method. - **A Posteriori Methods**: Describes the weighting method, ε-constraint method, hybrid method, method of weighted metrics, achievement scalarizing function approach, and other a posteriori methods. - **A Priori Methods**: Explores the value function method, lexicographic ordering, and goal programming. - **Interactive Methods**: Details various interactive methods such as the surrogate worth trade-off method, Geoffrion-Dyer-Feinberg method, sequential proxy optimization technique, Tchebycheff method, step method, reference point method, GUESS method, satisficing trade-off method, light beam search, reference direction approach, and NIMBUS method. **Part III: Related Issues** - **Comparing Methods**: Provides a comparative table of interactive methods and discusses method selection tools. - **Software**: Reviews available software for multiobjective optimization. - **Graphical Illustration**: Discusses methods for illustrating the Pareto optimal set and sets of alternatives. - **Future Directions**: Offers insights into future research directions. - **Epilogue**: Concludes the book with reflections on the field. The book aims to provide a consistent and up-to-date survey of nonlinear multiobjective optimization, suitable for researchers, students, and professionals in various fields. It includes a detailed bibliography and theoretical background, making it a valuable resource for both beginners and advanced readers.