# Algorithm for certain convex network problems

Jose Antonio Ventura, Cerry M. Klein

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

This paper presents an algorithm for solving network flow problems with a separable strictly convex quadratic objective function, and lower and upper bounds on the variables. An unconstrained dual problem is obtained by relaxing the network equality constraints. The dual problem is then solved by combining conjugate directions with a finite line search method. The main features of this technique are the simplification of matrix-vector products and the efficiency of the line-search step.

Original language English (US) 31-42 12 AMSE Review (Association for the Advancement of Modelling and Simulation Techniques in Enterprises) 8 2 Published - Dec 1 1988

### Fingerprint

Line Search
Dual Problem
Conjugate Directions
Network Flow Problem
Cross product
Matrix Product
Equality Constraints
Strictly Convex
Search Methods
Simplification
Upper and Lower Bounds
Objective function

### All Science Journal Classification (ASJC) codes

• Engineering(all)

### Cite this

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title = "Algorithm for certain convex network problems",
abstract = "This paper presents an algorithm for solving network flow problems with a separable strictly convex quadratic objective function, and lower and upper bounds on the variables. An unconstrained dual problem is obtained by relaxing the network equality constraints. The dual problem is then solved by combining conjugate directions with a finite line search method. The main features of this technique are the simplification of matrix-vector products and the efficiency of the line-search step.",
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year = "1988",
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}

Algorithm for certain convex network problems. / Ventura, Jose Antonio; Klein, Cerry M.

In: AMSE Review (Association for the Advancement of Modelling and Simulation Techniques in Enterprises), Vol. 8, No. 2, 01.12.1988, p. 31-42.

Research output: Contribution to journalArticle

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T1 - Algorithm for certain convex network problems

AU - Ventura, Jose Antonio

AU - Klein, Cerry M.

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Y1 - 1988/12/1

N2 - This paper presents an algorithm for solving network flow problems with a separable strictly convex quadratic objective function, and lower and upper bounds on the variables. An unconstrained dual problem is obtained by relaxing the network equality constraints. The dual problem is then solved by combining conjugate directions with a finite line search method. The main features of this technique are the simplification of matrix-vector products and the efficiency of the line-search step.

AB - This paper presents an algorithm for solving network flow problems with a separable strictly convex quadratic objective function, and lower and upper bounds on the variables. An unconstrained dual problem is obtained by relaxing the network equality constraints. The dual problem is then solved by combining conjugate directions with a finite line search method. The main features of this technique are the simplification of matrix-vector products and the efficiency of the line-search step.

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