A New Class of Feasible Direction Methods.
TEXAS UNIV AT AUSTIN CENTER FOR CYBERNETIC STUDIES
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This paper introduces a new class of feasible direction methods for solving differentiable convex programs with nonlinear convex constraints. The ones introduced here are based on two recent characterizations of optimality without a constraint qualification. The new methods are capable of generating feasible directions of descent along the boundary of the feasible set and they consistently give directions of steeper descent than many popular methods. This is achieved by solving only one linear program at each iteration. The new methods are particularly useful in solving large sparse convex programs some of the programs tested had 100 variables and 50 nonlinear constraints. Morever, the new methods are applicable whether or not Slaters condition or any other constraint qualification is satisfied.
- Theoretical Mathematics
- Operations Research