Download PDF by Dempe S.: A Bundle Algorithm Applied to Bilevel Programming Problems

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Additional info for A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions

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1 Syntax-Directed Semantics 25 An example of an attribute grammar As an example, we now specify the code semantics of programs in L( Gd in a syntax-directed way by means of an attribute grammar. It has the four meaning names code, temp, length, and name and one context name first. The carrier sets of code, temp, length, and name are the same domains as in the previous specification, and the carrier set of first is N. Again, code is the principal meaning name. The meaning names and context names are associated to the nonterminals by the mapping a as follows.

0 hold. , A and B are conjectured to be equal), then A ~ Band B ~ A hold. , A and B are guessed to be incomparable), then the inequalities A - B :f. 0 and B - A :f. 0 hold. Hence, given a conjecture for the inclusion diagram of H, we can construct a finite number of inclusions and inequalities whose validity is necessary and 46 2. Basic Notions and Notations sufficient to verify that our conjecture is the inclusion diagram of H. However, this finite number may be large even if the size of the conjectured diagram is relatively small.

Hence we can drop rank from the specification (a, rank) by just saying that a is a ranked set. , that wE a(k). Sometimes we also denote the rank function by rank n . In this book we will need an infinite supply of ranked symbols.

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A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions by Dempe S.


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