Dual Simplex Method

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 3 in In-Depth Analysis of Linear Programming, 2001, pp 119-166 from Springer

Abstract: Abstract Consider the canonical problem (3.1.1) % MathType!Translator!2!1!LaTeX.tdl!TeX -- LaTeX 2.09 and later! % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI % cacaWG4bGaaiykaiabg2da9maaamaabaGaam4yaiaacYcacaWG4baa % caGLPmIaayPkJaGaeyOKH4QaciyAaiaac6gacaGGMbGaaiilaiaadI % hacqGHiiIZcaWGybGaeyypa0ZaaiWaaeaacaWG4bGaeyicI4Saamyr % amaaCaaaleqabaGaamOBaaaakiaacQdacaWG4bGaeyyzImRaaGimai % aacYcacaWGbbGaamiEaiabg2da9iaadkgaaiaawUhacaGL9baaaaa!57AB! $$ f(x) = \left\langle {c,x} \right\rangle \to \inf ,x \in X = \left\{ {x \in {E^n}:x \ge 0,Ax = b} \right\} $$ where A is an m × n matrix, c ∈ E n , b ∈ E m . Let r = rank A = m. We shall give one more method for solving this problem which is customarily called a dual simplex method [1, 75]. In literature this method is also known as the method of successive refinement of estimates [98]. In what follows, we shall call the simplex method with anticyclin described in Chapter 1 the main simplex method.

Keywords: Extreme Point; Initial Point; Dual Problem; Simplex Method; Supporting Point (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_3

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DOI: 10.1007/978-94-015-9759-3_3

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