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An interior point algorithm for large scale nonlinear programming
 SIAM Journal on Optimization
, 1999
"... The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primaldual versions of t ..."
Abstract

Cited by 74 (17 self)
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The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primaldual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests. Key words: constrained optimization, interior point method, largescale optimization, nonlinear programming, primal method, primaldual method, successive quadratic programming, trust region method.
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 tractab ..."
Abstract

Cited by 3 (0 self)
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. 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, largescale optimization, nonlinear programming The most important open problem in nonlinear optimization is the solution of large constrained problems of the form minimize f(x) subject to h(x) = 0 (1) g(x) 0; where the functions f : R n ! R; h : R n ! R m and g : R n ! R t are assumed to be smooth. Assuming t...