Regularization Methods

F. P. Vasilyev and A. Yu. Ivanitskiy
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F. P. Vasilyev: Moscow State University
A. Yu. Ivanitskiy: Chuvash State University

Chapter Chapter 5 in In-Depth Analysis of Linear Programming, 2001, pp 203-228 from Springer

Abstract: Abstract In this chapter we consider the primal linear programming problem (5.1.1) % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI % cacaWG4bGaaiykaiabg2da9maaamaabaGaam4yaiaacYcacaWG4baa % caGLPmIaayPkJaGaeyOKH4QaciyAaiaac6gacaGGMbGaaiilaiaayw % W7caWG4bGaeyicI4Saamiwaiabg2da9maacmaabaGaamiEaiabgIGi % olaadweadaahaaWcbeqaaiaad6gaaaGccaGG6aGaamiEaiabgwMiZk % aaicdacaGGSaGaamyqaiaadIhacqGHKjYOcaWGIbaacaGL7bGaayzF % aaaaaa!59E8! $$ f(x) = \left\langle {c,x} \right\rangle \to \inf ,\quad x \in X = \left\{ {x \in {E^n}:x \ge 0,Ax \le b} \right\} $$ , where A = {a ij } are m × n matrices, b = (b 1,…,b m )⊤ ∈ E m , c = (c 1,…,c n )⊤ ∈ E n . We assume that X ≠ ∅, f * = inf x ∈X f(x) > -∞. Then, according to Theorem 2.1.1, X * = {x ∈ X : f(x) = f *} ≠ ∅.

Keywords: Dual Problem; Linear Programming Problem; Regularization Method; Primal Problem; Normal Solution (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9759-3_5

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DOI: 10.1007/978-94-015-9759-3_5

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