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Stefan M. Stefanov ()
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Stefan M. Stefanov: South-West University Neofit Rilski

Chapter Chapter 10 in Separable Optimization, 2021, pp 181-191 from Springer

Abstract: Abstract If it is allowed for problem (C): i) $$d_j'(x_j) \equiv 0$$ d j ′ ( x j ) ≡ 0 or ii) $$d_j'(x_j) \not \equiv 0$$ d j ′ ( x j ) ≢ 0 but $$d_j'(a_j) = 0$$ d j ′ ( a j ) = 0 and/or $$d_j'(b_j) = 0$$ d j ′ ( b j ) = 0 for some $$j \in J$$ j ∈ J in (5.2), then for such j’s, we cannot construct the expressions $$ -{c_j'(a_j) \over d_j'(a_j)}$$ - c j ′ ( a j ) d j ′ ( a j ) and/or $$-{c_j'(b_j) \over d_j'(b_j)}$$ - c j ′ ( b j ) d j ′ ( b j ) , by means of which the sets $$J_a^\lambda \> (5.4), J_b^\lambda \> (5.5), J^\lambda \> (5.6)$$ J a λ ( 5.4 ) , J b λ ( 5.5 ) , J λ ( 5.6 ) are defined. In case i) we have $$d_j(x_j) =: d_j = const$$ d j ( x j ) = : d j = c o n s t and $$x_j$$ x j ’s are not involved in (5.2) for such j’s.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-78401-0_10

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DOI: 10.1007/978-3-030-78401-0_10

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