By Dimitri Bertsekas, Angelia Nedic, Asuman Ozdaglar
A uniquely pedagogical, insightful, and rigorous remedy of the analytical/geometrical foundations of optimization. between its unique gains, the e-book: 1) Develops carefully and comprehensively the idea of convex units and features, within the classical culture of Fenchel and Rockafellar 2) offers a geometrical, hugely visible remedy of convex and nonconvex optimization difficulties, together with lifestyles of options, optimality stipulations, Lagrange multipliers, and duality three) contains an insightful and accomplished presentation of minimax conception and nil sum video games, and its reference to duality four) Describes twin optimization, the linked computational tools, together with the unconventional incremental subgradient tools, and purposes in linear, quadratic, and integer programming five) includes many examples, illustrations, and workouts with entire recommendations (about two hundred pages) published on the web. From the preface: This publication specializes in the idea of convex units and features, and its connections with a couple of subject matters that span a huge variety from non-stop to discrete optimization. those issues comprise Lagrange multiplier concept, Lagrangian and conjugate/Fenchel duality, minimax idea, and nondifferentiable optimization. The ebook advanced from a suite of lecture notes for a graduate path at M.I.T. it truly is well known that, other than being an eminently valuable topic in engineering, operations study, and economics, convexity is a superb car for assimilating a number of the simple ideas of actual research inside of an intuitive geometrical atmosphere. regrettably, the subject's assurance in educational curricula is scant and incidental. We think that not less than a part of the reason being the dearth of textbooks which are compatible for lecture room guide, quite for nonmathematics majors. we now have hence attempted to make convex research available to a broader viewers by way of emphasizing its geometrical personality, whereas retaining mathematical rigor. we've got integrated as many insightful illustrations as attainable, and we've used geometric visualization as a vital instrument for keeping the scholars' curiosity in mathematical proofs. Our remedy of convexity concept is sort of entire, with all significant elements of the topic receiving gigantic therapy. The mathematical must haves are a direction in linear algebra and a direction in actual research in finite dimensional areas (which is the specific surroundings of the book). A precis of this fabric, with no proofs, is supplied in part 1.1. The insurance of the speculation has been considerably prolonged within the workouts, which characterize a huge section of the booklet. particular ideas of all of the workouts (nearly 2 hundred pages) are internet-posted within the book's www web page the various routines might be tried through the reader with out taking a look at the ideas, whereas others are demanding yet will be solved through the complex reader with the help of tricks. nonetheless different routines characterize enormous theoretical effects, and every now and then contain new and unpublished study. Readers and teachers may still come to a decision for themselves how one can make most sensible use of the internet-posted strategies. a major a part of our process has been to take care of a detailed hyperlink among the theoretical remedy of convexity and its software to optimization.