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Mathematical developments arising from linear programming : [electronic resource] proceedings of a joint summer research conference held at Bowdoin College, June 25-July 1, 1988 / Jeffrey C. Lagarias and Michael J. Todd, editors.

By: AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Developments Arising from Linear Programming (1988 : Bowdoin College)Contributor(s): Lagarias, Jeffrey C, 1949- | Todd, Michael J, 1947-Material type: Text

TextSeries: Contemporary mathematics (American Mathematical Society) ; v. 114.Publication details: Providence, R.I. : American Mathematical Society, c1990Description: 1 online resource (xiv, 341 p.)ISBN: 9780821877029 (online)Subject(s): Programming (Mathematics) -- Congresses | Linear programming -- CongressesAdditional physical formats: Mathematical developments arising from linear programming :DDC classification: 519.7/2 LOC classification: QA402.5 | .A454 1988Online resources: Contents | Contents

Contents:

Some recent results on convex polytopes / Carl W. Lee -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097862 Probabilistic analysis of the simplex method / Karl-Heinz Borgwardt -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097863 On solving the linear programming problem approximately / Nimrod Megiddo -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097864 Riemannian geometry underlying interior-point methods for linear programming / Narendra Karmarkar -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097865 Steepest descent, linear programming, and Hamiltonian flows / A. M. Bloch -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097866 An $O(n^3L)$ potential reduction algorithm for linear programming / Yinyu Ye -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097867 I. I. Dikin's convergence result for the affine-scaling algorithm / R. J. Vanderbei and J. C. Lagarias -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097868 Phase $1$ search directions for a primal-dual interior point method for linear programming / Irvin J. Lustig -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097869 Some results concerning convergence of the affine scaling algorithm / Earl R. Barnes -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097870 Dual ellipsoids and degeneracy in the projective algorithm for linear programming / Kurt M. Anstreicher -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097871 A note on limiting behavior of the projective and the affine rescaling algorithms / Miroslav D. A�si�c, Vera V. Kova�cevi�c-Vuj�ci�c and Mirjana D. Radosavljevi�c-Nikoli�c -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097872 On the convergence behavior of trajectories for linear programming / Christoph Witzgall, Paul T. Boggs and Paul D. Domich -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097873 Limiting behavior of the affine scaling continuous trajectories for linear programming problems / Ilan Adler and Renato D. C. Monteiro -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097874 Convergence and boundary behavior of the projective scaling trajectories for linear programming / Renato D. C. Monteiro -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097875 On the complexity of a numerical algorithm for solving generalized convex quadratic programs by following a central path / F. Jarre, G. Sonnevend and J. Stoer -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097876 Canonical problems for quadratic programming and projective methods for their solution / Bahman Kalantari -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097877 An interior point algorithm for solving smooth convex programs based on Newton's method / Sanjay Mehrotra and Jie Sun -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097878 A modified Kantorovich inequality for the convergence of Newton's method / A. A. Goldstein -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097879 An interior-point approach to NP-complete problems. I / Narendra Karmarkar -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097880 Solving matching problems using Karmarkar's algorithm / John E. Mitchell and Michael J. Todd -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097881 Efficient faces of polytopes: interior point algorithms, parameterization of algebraic varieties, and multiple objective optimization / S. S. Abhyankar, T. L. Morin and T. Trafalis -- http://www.ams.org/conm/114/ http://dx.doi.org/10.1090/conm/114/1097882

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"The AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Developments Arising from Linear Programming was held at Bowdoin College, Brunswick, Maine, on June 25-July 1, 1988"--T.p. verso.

Includes bibliographical references.

Some recent results on convex polytopes / Carl W. Lee -- Probabilistic analysis of the simplex method / Karl-Heinz Borgwardt -- On solving the linear programming problem approximately / Nimrod Megiddo -- Riemannian geometry underlying interior-point methods for linear programming / Narendra Karmarkar -- Steepest descent, linear programming, and Hamiltonian flows / A. M. Bloch -- An $O(n^3L)$ potential reduction algorithm for linear programming / Yinyu Ye -- I. I. Dikin's convergence result for the affine-scaling algorithm / R. J. Vanderbei and J. C. Lagarias -- Phase $1$ search directions for a primal-dual interior point method for linear programming / Irvin J. Lustig -- Some results concerning convergence of the affine scaling algorithm / Earl R. Barnes -- Dual ellipsoids and degeneracy in the projective algorithm for linear programming / Kurt M. Anstreicher -- A note on limiting behavior of the projective and the affine rescaling algorithms / Miroslav D. A�si�c, Vera V. Kova�cevi�c-Vuj�ci�c and Mirjana D. Radosavljevi�c-Nikoli�c -- On the convergence behavior of trajectories for linear programming / Christoph Witzgall, Paul T. Boggs and Paul D. Domich -- Limiting behavior of the affine scaling continuous trajectories for linear programming problems / Ilan Adler and Renato D. C. Monteiro -- Convergence and boundary behavior of the projective scaling trajectories for linear programming / Renato D. C. Monteiro -- On the complexity of a numerical algorithm for solving generalized convex quadratic programs by following a central path / F. Jarre, G. Sonnevend and J. Stoer -- Canonical problems for quadratic programming and projective methods for their solution / Bahman Kalantari -- An interior point algorithm for solving smooth convex programs based on Newton's method / Sanjay Mehrotra and Jie Sun -- A modified Kantorovich inequality for the convergence of Newton's method / A. A. Goldstein -- An interior-point approach to NP-complete problems. I / Narendra Karmarkar -- Solving matching problems using Karmarkar's algorithm / John E. Mitchell and Michael J. Todd -- Efficient faces of polytopes: interior point algorithms, parameterization of algebraic varieties, and multiple objective optimization / S. S. Abhyankar, T. L. Morin and T. Trafalis --