Ebook: Progress in Mathematical Programming: Interior-Point and Related Methods

The starting point of this volume was a conference entitled "Progress in Mathematical Programming", held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarka's algorithm. Presentations included new algorithms, new analysis of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming.

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The starting point of this volume was a conference entitled "Progress in Mathematical Programming", held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarka's algorithm. Presentations included new algorithms, new analysis of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming.
Content:
Front Matter....Pages i-x
An Algorithm for Solving Linear Programming Problems in O(n 3 L) Operations....Pages 1-28
A Primal-Dual Interior Point Algorithm for Linear Programming....Pages 29-47
An Extension of Karmarkar’s Algorithm and the Trust Region Method for Quadratic Programming....Pages 49-63
Approximate Projections in a Projective Method for the Linear Feasibility Problem....Pages 65-78
A Locally Weil-Behaved Potential Function and a Simple Newton-Type Method for Finding the Center of a Polytope....Pages 79-90
A Note on Comparing Simplex and Interior Methods for Linear Programming....Pages 91-103
Pricing Criteria in Linear Programming....Pages 105-129
Pathways to the Optimal Set in Linear Programming....Pages 131-158

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The starting point of this volume was a conference entitled "Progress in Mathematical Programming", held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarka's algorithm. Presentations included new algorithms, new analysis of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming.
Content:
Front Matter....Pages i-x
An Algorithm for Solving Linear Programming Problems in O(n 3 L) Operations....Pages 1-28
A Primal-Dual Interior Point Algorithm for Linear Programming....Pages 29-47
An Extension of Karmarkar’s Algorithm and the Trust Region Method for Quadratic Programming....Pages 49-63
Approximate Projections in a Projective Method for the Linear Feasibility Problem....Pages 65-78
A Locally Weil-Behaved Potential Function and a Simple Newton-Type Method for Finding the Center of a Polytope....Pages 79-90
A Note on Comparing Simplex and Interior Methods for Linear Programming....Pages 91-103
Pricing Criteria in Linear Programming....Pages 105-129
Pathways to the Optimal Set in Linear Programming....Pages 131-158
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