Optimization by Vector Space Methods 1969th Edition

I have used this book since it first appeared. I first went through it in seminar when I was a graduate student in 1970 and have since used it in many different courses. I require my gradaute students to read and understand it. It is very easy to read and give the best picture of optimization that I know of. I expect that this book will be required in most economics and engineering programs for the next 40 years. Luenberger is a master expositor--it is to bad that more books are not written in this style.

Hope it was cheaper though.

Optimization by Vector Space Methods, by David Luenberger, is one of the finest math texts I have ever read, and I've read hundreds. Many years ago this book sparked my interest in optimization and convinced me that the abstract mathematics I had been immersed in actually would be applicable to real problems. Since then, Luenberger's book has inspired several of my graduate students. I merely lent them my copy, and Luenberger did the rest; he drew them in by carefully laying the foundation for an elegant theory, with just the right mix of formalism and intuition, and opened their eyes to the beauty and practicality of abstract mathematics. Anyone with an interest in higher-level mathematics (beyond multi-variable calculus, say) would benefit from exposure to this finely-crafted book. I daresay, the rampant math anxiety that is so prevalent in the West would be substantially reduced if more authors would take such meticulous care in presenting their material.The format of Luenberger's book is also extremely appealing in a way that I cannot quite put my finger on. The typography and illustrations are inherently crisp and inviting; they draw you in. There is nothing at all superfluous or gratuitous in this book. It is utterly to-the-point, methodical, and above all, clear. The techniques are developed starting from an elementary treatment of vector spaces, then proceeding on to Banach spaces and Hilbert spaces. Along the way, Luenberger introduces convexity, cones, basic topology, random variables, minimum-variance estimators, and least squares, among many other things. There is a recurring theme of duality, which can be used in a way analogous to the inner product of a Hilbert space. In particular, the familiar projection theorems of Hilbert spaces can be echoed in simpler normed linear spaces using duality, which Luenberger motivates and covers beautifully.The book also covers some of the standard fare of functional analysis, such as the Han-Banach theorem, strong and weak convergence, and the Banach inverse theorem. However, Luenberger never wanders too far off into abstract nonsense; around every corner lay tantalizing application of these ideas to optimization. Luenberger first explores optimization of functionals then covers constrained optimization, which builds upon concepts such as positive cones and Lagrange multipliers. The optimization methods themselves have endless applications in fields such as computer vision, computer graphics, economics, and physics. Indeed, the list is effectively endless as optimization techniques pervade math and science.I'm certain that the appeal of this book is helped immeasurably by the inherent beauty of the subject matter. Hilbert-space methods are lovely in themselves--they possess a structure that engages one's geometric intuition while at the same time admitting convenient algebraic properties. Once you are in the habit of phrasing problems in abstract settings such as Hilbert spaces, it forever changes how you look at things; you cannot help but look past the clutter to the essence of a problem (or, at least try very hard to do so). While this material is not nearly as abstract as, say, category theory, it nevertheless hits a high point in mathematics--a point more people ought to experience.If you've had some exposure to optimization methods, or need to apply them in the context of computer vision, graphics, or finance, to mention just a few areas, then I urge you to take a look at Luenberger's fine book. It too hits a high point in clarity of mathematical writing. Combine beautiful theory with endless applications and lucid writing, and you have a winner of a book.

This is a true classic in the field of optimization, a timeless and definitive book that is hard to match in terms of quality and effectiveness of exposition. It shows that a large segment of the field can be effectively unified by a few geometric principles of linear vector space theory. It helps serious students of optimization to appreciate the unifying power of sophisticated mathematics, and it also provides an accessible and highly motivating vehicle for studying these mathematics. A measure of the quality of this book is that despite its success, it has not been emulated by any other book.

This is a perfect book to study in detail. Prof. Luenberger brings a set of topics in analysis that is related to optimization into one coherent exposition. I took a graduate course using this book with a great professor. I must say that the experience is an eye opener for me. The topics are very interesting and well motivated, the proofs are elegant. It keeps on delighting chapter after chapter. I can't overstate the enthusiasm the book generated in me to study mathematics further. The book is absolutely the best.

When I decided to change my career path from B-school to mathematics, I know that only with taking calculus and linear algebra courses is definitely not enough for me to get into a decent math graduate program. I spent an afternoon in a local bookstore to find a book for functional analysis and Hilbert space which is comprehensible for me at that time. I found Luenberger. I was obsessed with its clarity and simplicity without sacrificing too much rigor. Especially for those finance student who want to learn some advanced math for quant finance but may not have enough background to deal with, Luenberger's book is a really good starting point!

This book is a timeless classic, filled with extraordinarily powerful mathematics and applicable to just about every serious subject area. Luenberger did a masterful job of writing a book that will "unravel the spaghetti" seen in most other books. The visual perspectives he provides to seemingly abstract ideas are the key.

I owe Dr Luenberger a million thanks for writing this book. As his student, I think he is the master of putting complex issues in simple words. Your faithful student..Jayanth Krishnan

Excelente libro

This book is an absolute classic. I especially value the clear progression from abstract mathematical conceptsto practical applications.