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TY - CHAP
TI - A Basic Optimization Problem in Simplified Form
A2 - Neustadt, Lucien W.
AB - This chapter is in many ways a capsule version of the entire book. We shall here investigate the optimization problem which consists in finding the minimum of a function*ϕ*^{0}on a given set${\cal {E}}$, subject to equality constraints*φ*^{i}(*e*) = 0 for*i*= 1,…,*m*and inequality constraints*ϕ*^{i}(*e*) ≤ 0 for*i*= 1,…,*μ*, where*φ*^{1},…,*φ*^{m},*ϕ*^{0},*ϕ*^{1},…,*ϕ*^{μ}are given, real-valued functions defined on${\cal {E}}$. Under the assumptions that${\cal {E}}$is a subset of a linear vector space which is finitely open in itself [see (I.1.39)], that*φ*^{1},…,*φ*^{m}are finitely differentiable

EP - 95
PB - Princeton University Press
PY - 1976
SN - null
SP - 63
T2 - Optimization: A Theory of Necessary Conditions
UR - http://www.jstor.org/stable/j.ctt13x1f6d.6
Y2 - 2021/09/17/
ER -