Titlebook: Optimization; Kenneth Lange Textbook 2013Latest edition Springer Science+Business Media New York 2013 Convexity.Differentiation.Gauge Inte

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The EM Algorithm,e can often solve the M step analytically. The price we pay for this simplification is that the EM algorithm is iterative. Reconstructing the missing data is bound to be slightly wrong if the parameters do not already equal their maximum likelihood estimates.

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Textbook 2013Latest editionnt, and the calculus of variations. Convex calculus is now treated in much greater depth.  Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with

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Analysis of Convergence,icity. Scoring lies somewhere between Newton’s method and the MM algorithm. It tends to converge more quickly than the MM algorithm and to behave more stably than Newton’s method. Quasi-Newton methods also occupy this intermediate zone. Because the issues are complex, all of these algorithms survive and prosper in certain computational niches.

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Penalty and Barrier Methods,methods, it is gradually sent to 0. Nothing prevents one from assigning different tuning constants to different penalties or barriers in the same problem. Either strategy generates a sequence of solutions that converges in practice to the solution of the original constrained optimization problem.

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,The Seven C’s of Analysis,zation. However, painful experience and exotic counterexamples have taught mathematicians to pay attention to details. Fortunately, we can benefit from the struggles of earlier generations and bypass many of the intellectual traps.

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Differentiation,tion of differentiability that avoids most of the pitfalls and makes differentiation of vectors and matrices relatively painless. In later chapters, this definition also improves the clarity of exposition.

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Karush-Kuhn-Tucker Theory, is called the objective function, the functions . are called equality constraints, and the functions . are called inequality constraints. Any point . satisfying all of the constraints is said to be feasible.