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- W2079155874 abstract "Abstract The paper considers the following unconstrained optimization problem: minimize f n ( x n , n ) = g n ( x n ) + h ( n ), where g n ( x n ) = αϵ i = 0 n −1 ∫ x i x i = 1 [ ∫ x x i + 1 b ( t ) d( t )]d x , over both the variables x 1 , x 2 , …, x n −1 , and their number n , when x 0 , x n ≡ X are known boundary conditions, and h ( n ) is increasing, unbounded and weakly convex. Examples that demonstrate the practical usefulness of this decision process are given, and a two-phase approach for solving it, namely, minimize first over the arguments for a fixed n , and then over n , is suggested. Simple conditions, for a general g n ( x n ), under which phase II can be carried out by a finite search are stated, and then the question: “Under what circumstances does the search for the optimal n reduce to a simple condition?” is posed. Kuhn-Tucker type two-phase optimality conditions that answer this question are established, and moreover, specifications on the dominating single variable function b ( x ) for which the conditions hold are set forth." @default.
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- W2079155874 date "1984-03-01" @default.
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- W2079155874 title "A decision process over variables and their number: Two-phase optimality conditions" @default.
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- W2079155874 doi "https://doi.org/10.1016/0377-2217(84)90109-7" @default.
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