Titlebook: Convex Analysis and Global Optimization; Hoang Tuy Book 19981st edition Springer Science+Business Media Dordrecht 1998 Approximation.Mathe

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書目名稱Convex Analysis and Global Optimization影響因子(影響力)




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書目名稱Convex Analysis and Global Optimization讀者反饋




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Obedient

Outer and Inner Approximation in such a way that the sequence of solutions of these relaxed problems converges to a solution of the given problem. This approach, first introduced in convex programming in the late fifties (Cheney and Goldstein (1959), Kelley (1960)) was later extended, under the name of ., to concave minimizatio

驕傲

Decompositioniables. However not all the variables play an equal part in the “curse of dimensionality”. Variables which enter the problem in a convex way, i.e. such that the problem becomes convex when all the other variables are fixed, are often relatively “easy”. The main source of difficulty comes from the “n

MUTED

發(fā)生

RADE

RADE

Violence and Visibility in Modern HistoryConvexity is a nice property of functions which, unfortunately, is not preserved even under such simple algebraic operations as scalar mutiplication or lower envelope. In this chapter we introduce the . (also called the .) which is the common underlying mathematical structure of virtually all nonconvex optimization problems.

GROWL

Violence and Visibility in Modern HistoryWe will be concerned with optimization problems of the general form.where . is a closed convex set in .., .: Ω→ . and ..: Ω→., . 1,…,. are functions defined on some set Ω in .. containing .. Denoting the . by .:.we can also write the problem as

adipose-tissue

Convex SetsLet . be two points of ... The set of all . ∈.. of the form.is called the .. A subset . of .. is called an . (or .) if it contains every line through any two points of it, i.e. if (1 — λ). + λ. ∈ . for every . ∈ ., . ∈. and every λ ∈ .. An affine set which contains the origin is a subspace.

胎兒