On the behavior of Lagrange multipliers in convex and nonconvex infeasible interior point methods
نویسندگان
چکیده
منابع مشابه
On the behavior of Lagrange multipliers in convex and non-convex infeasible interior point methods∗
This paper analyzes sequences generated by infeasible interior point methods. In convex and nonconvex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We also show ...
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Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that κ̄(ζ) = 1 (Conjecture 5.1 in [1]), which is a factor of √ 2n better than has been proved in [1], and which would yield an O( √ n) iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that κ̄(ζ) is in the order of...
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We study interior-point methods for optimization problems in the case of infeasibility or unboundedness. While many such methods are designed to search for optimal solutions even when they do not exist, we show that they can be viewed as implicitly searching for well-defined optimal solutions to related problems whose optimal solutions give certificates of infeasibility for the original problem...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2019
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-019-01454-4