Alexander Shapiro - Böcker

In this book on Richard Wagner’s compelling but enigmatic masterpiece Götterdämmerung, the final opera of his monumental Ring tetralogy, Alexander H. Shapiro advances an ambitious new interpretation which uncovers intriguing new facets to the work’s profound insights into the human condition. By taking a fresh look at the philosophical and historical influences on Wagner, and critically reevaluating the composer’s intellectual worldview as revealed in his own prose works, letters, and diary entries, the book challenges a number of conventional views that continue to impede a clear understanding of this work’s meaning. The book argues that Götterdämmerung, and hence the Ring as a whole, achieves coherence when interpreted in terms of contemporary nineteenth-century theories of progress, and, in particular, G.W.F. Hegel’s philosophies of mind and history. A central target of the book is the article of faith that has come to dominate Wagner scholarship over the years – that Wagner’s encounter in 1854 with Arthur Schopenhauer’s philosophy conclusively altered the final message of the Ring from one of historical optimism to existential pessimism. The author contends that Schopenhauer’s uncompromising denigration of the will and denial of the possibility for human progress find no place in the written text of the Ring or in a plausible reading of the final musical setting. In its place, the author discovers in the famous Immolation Scene a celebration of mankind’s inexhaustible capacity for self-improvement and progress. The author makes the further compelling case that this message of progress is communicated not through Siegfried, the traditional male hero of the drama, but through Brünnhilde, the warrior goddess who becomes a mortal woman. In her role as a battle-tested world-historical prophet she is the true revolutionary change agent of Wagner’s opera who has the strength and vision to comprehend and thereby shape human history. This highly lucid and accessible study is aimed not only at scholars and researchers in the fields of opera studies, music and philosophy, and music history, but also Wagner enthusiasts, and readers and students interested in the history and philosophy of the nineteenth century.

This book presents general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems. These results may be applied to various fields, from physics to economics, as various examples in the book show. Therefore, the book is an opportunity for popularizing these techniques among researchers involved in other sciences. Consequently the readership should be not only researchers in the field of optimization, nonlinear programming and optimal control, but also users of optimization in a wide sense, in mechanics (elasticity and plasticity theory), physics, statistics, finance and economics. The book will be useful to research professionals, including graduate students at an advanced level.

In this book on Richard Wagner’s compelling but enigmatic masterpiece Götterdämmerung, the final opera of his monumental Ring tetralogy, Alexander H. Shapiro advances an ambitious new interpretation which uncovers intriguing new facets to the work’s profound insights into the human condition. By taking a fresh look at the philosophical and historical influences on Wagner, and critically reevaluating the composer’s intellectual worldview as revealed in his own prose works, letters, and diary entries, the book challenges a number of conventional views that continue to impede a clear understanding of this work’s meaning. The book argues that Götterdämmerung, and hence the Ring as a whole, achieves coherence when interpreted in terms of contemporary nineteenth-century theories of progress, and, in particular, G.W.F. Hegel’s philosophies of mind and history. A central target of the book is the article of faith that has come to dominate Wagner scholarship over the years – that Wagner’s encounter in 1854 with Arthur Schopenhauer’s philosophy conclusively altered the final message of the Ring from one of historical optimism to existential pessimism. The author contends that Schopenhauer’s uncompromising denigration of the will and denial of the possibility for human progress find no place in the written text of the Ring or in a plausible reading of the final musical setting. In its place, the author discovers in the famous Immolation Scene a celebration of mankind’s inexhaustible capacity for self-improvement and progress. The author makes the further compelling case that this message of progress is communicated not through Siegfried, the traditional male hero of the drama, but through Brünnhilde, the warrior goddess who becomes a mortal woman. In her role as a battle-tested world-historical prophet she is the true revolutionary change agent of Wagner’s opera who has the strength and vision to comprehend and thereby shape human history. This highly lucid and accessible study is aimed not only at scholars and researchers in the fields of opera studies, music and philosophy, and music history, but also Wagner enthusiasts, and readers and students interested in the history and philosophy of the nineteenth century.

The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.

Optimization problems involving stochastic models occur in most areas of science and engineering, particularly telecommunications, medicine, and finance. Their existence reveals a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In this second edition, the authors introduce new material to reflect recent developments, including: analytical descriptions of the tangent and normal cones of chance constrained sets; analysis of optimality conditions for nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and an in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results. This book is intended for researchers working in optimization. It is also suitable for advanced graduate courses in this area.