An algorithm for linearly constrained nonlinear programming problems

AbstractIn this paper an algorithm for solving a linearly constrained nonlinear programming problem is developed. Given a feasible point, a correction vector is computed by solving a least distance programming problem over a polyhedral cone defined in terms of the gradients of the “almost” binding constraints. Mukai's approximate scheme for computing the step size is generalized to handle the constraints. This scheme provides an estimate for the step size based on a quadratic approximation of the function. This estimate is used in conjunction with Armijo line search to calculate a new point. It is shown that each accumulation point is a Kuhn-Tucker point to a slight perturbation of the original problem. Furthermore, under suitable second order optimality conditions, it is shown that eventually only one trial is needed to compute the step size

Structure and function in flow networks

Peer reviewedPublisher PD

Linear Programming and Network Flows

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Note--On the Use of Fictitious Bounds in Tree Search Algorithms

One of the strategies used by many tree search algorithms is to follow down one path in the tree until either a feasible solution is found or else fathoming occurs. For a minimization problem, the lower bounds calculated at various tree nodes tend to be well below the optimal value of the objective function, let alone the values of the successively improving upper bounds. As a result fathoming usually occurs only deep in the tree, and consequently, the search becomes rather lengthy. The purpose of this note is to describe a procedure for using and updating fictitious upper bounds in a systematic way so that optimal and suboptimal solutions can be obtained with a smaller computational effort. The procedure is illustrated by two examples: the traveling salesman problem and the quadratic assignment problem.

Linear Programming and Network Flows

The authoritative guide to modeling and solving complex problems with linear programming-extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations researc