Titlebook: Nondifferentiable and Two-Level Mathematical Programming; Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard Book 1997 Springer Science+Busines

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978-1-4613-7895-2Springer Science+Business Media New York 1997

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Differentiable Nonlinear Programming,In this chapter we deal with the following basic optimization problem: Among the n-tuples (..,…, ..) that satisfy in . inequalities .. (.., …,..) . 0, . = 1,…, ., and ℓ equalities .. (..,…, ..) = 0, . = 1,…, ℓ, find a solution (.) which minimizes the function . (..,…,..).

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General Resource Allocation Problem for Decentralized Systems,In a decentralized system, overall optimization is achieved from a central point of view but each subsystem is invested with considerable power. Such a system is characterized by multiple decision makers in the subsystems, each of whom can exercise strong initiatives at the local level in pursuit of its own goal.

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https://doi.org/10.1007/978-1-4615-6305-1algorithm; algorithms; complex system; complex systems; linear optimization; mathematical programming; non

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Mathematical Preliminaries, to show that they are . or .. Vectors are . oriented unless otherwise specified. For two vectors.the .,., of . and . is denoted by .... Superscript . stands for the .. When . is a row vector, we write the inner product as . • ..

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The Stackelberg Problem: Linear and Convex Case,ing problem (BLPP). In this chapter we present several of the most successful algorithms that have been developed for this case, and when possible, compare their performance. We begin with some basic notation and a discussion of the theoretical character of the problem.