1996 | OriginalPaper | Buchkapitel
Adaptive Stochastic Optimization Procedures
verfasst von : János D. Pintér
Erschienen in: Global Optimization in Action
Verlag: Springer US
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Consider the following stochastic programming problem: 3.6.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeaabmqaaa % qaaiGac2gacaGGPbGaaiOBaiaadweacaWGMbWaaSbaaSqaaiaaicda % aeqaaOWaaeWaaeaacaWG4bGaaiilaiaadMhaaiaawIcacaGLPaaaae % aacaWGfbGaamOzamaaBaaaleaacaWGPbaabeaakmaabmaabaGaamiE % aiaacYcacaWG5baacaGLOaGaayzkaaGaeyizImQaaGimaiaacYcaca % aMf8UaamyAaiabg2da9iaaigdacaGGSaGaeSOjGSKaaiilaiaadMea % caGGSaaabaGaamiEaiabgIGiolaadseadaWgaaWcbaGaaGimaaqaba % GccqGHckcZtuuDJXwAK1uy0HMmaeHbfv3ySLgzG0uy0HgiuD3BaGqb % biab-1risjab-bW9UnaaCaaaleqabaGaamOBaaaakiaacYcacaaMf8 % UaamyEamaabmaabaGaam4DaaGaayjkaiaawMcaaiabgIGiolab-1ri % snaaCaaaleqabaGaamyCaaaakiaac6caaaaaaa!7052!<Equation ID="Equ1"><EquationNumber>1</EquationNumber><EquationSource Format="MATHTYPE"><![CDATA[ $$\begin{array}{*{20}{c}} {\min E{{f}_{0}}\left( {x,y} \right)} \hfill \\ {E{{f}_{i}}\left( {x,y} \right) \leqslant 0,\quad i = 1, \ldots ,I,} \hfill \\ {x \in {{D}_{0}} \subset \mathbb{R}{{}^{n}},\quad y\left( w \right) \in {{\mathbb{R}}^{q}}.} \hfill \\ \end{array}$$ In (3.6.1), x is a decision vector to be selected from a closed, bounded subset D0 of the n-dimensional real Euclidean space ℝn; y is a q-dimensional vector valued random variable; f i , i = 0, 1,...,I, are respectively defined measurable functions; E is the symbol of mathematical expectation (the expected values are supposed to exist). Note that (3.6.1) is a fairly general stochastic programming model form; it encompasses—under suitable transformations—the ‘model block’ and types discussed in the previous chapter.