The {open_quotes}Hot{close_quotes} start phenomenon in constrained optimization

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:36401

Polyak, B

The Modified Barrier and Modified Interior Centers Methods are producing a primal-dual sequence that converges to the prime-dual solution due to the Lagrange multipliers update, while both the barrier parameter and the center are fixed. Therefore, the condition number of the Modified Barrier or Modified Distance functions Hessians are stable when the prime-dual approximations approach, the solution, and so is the area around the primal minimizers where the Newton Method is {open_quotes}well defined{close_quotes}. Therefore, for any nondegenerate constrained optimization problem it comes to a point - {open_quotes}hot start{close_quotes} - when only O(lnln{sup -1}) Newton steps ({epsilon} > 0 is the desired accuracy) is enough for a Lagrange multipliers update, which shrinks the distance to the primal-dual solution by a factor 0 < q < 1. We will characterize the {open_quotes}hot start{close_quotes} analytically and provide numerical results that strongly collaborate the theory.

• OSTI ID: 36401
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ALGORITHMS
CONVERGENCE
MATRICES
NUMERICAL SOLUTION
OPTIMIZATION
VARIATIONAL METHODS