DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 667-676

Richard H. Byrd and Jorge Nocedal

Title: Active Set and Interior Methods for Nonlinear Optimization

We discuss several fundamental questions concerning the problem of minimizing a nonlinear function subject to a set of inequality constraints. We begin by asking: What makes the problem intrinsically difficult to solve, and which characterizations of the solution make its solution more tractable? This leads to a discussion of two important methods of solution: active set and interior points. We make a critical assessment of the two approaches, and describe the main issues that must be resolved to make them effective in the solution of very large problems.

1991 Mathematics Subject Classification: 65K05 90C30

Keywords and Phrases: nonlinear optimization, large-scale optimization, nonlinear programming

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