Local optimum, definition

Give definitions for the following maximum, minimum, optimum, unimodal, multimodal, local optimum, global optimum, continuous, discrete, constraint, equality constraint, inequality constraint, lower bound, upper bound, natural constraint, artificial constraint, degree of freedom, feasible region, nonfeasible region, factor tolerance. 

Give definitions for the following terms unimodal multimodal replication of experiments factor level coding of factors local and global optimum randomization screening designs factor effects. 

Earlier observations by Cesario et al. [60] of a decay in fluorescence for arrays of Au nanoparticles spaced above a Ag film by a Si02 layer of increasing thickness, were interpreted as due to the finite vertical extent of the evanescent fields associated with a surface plasmon. In this model the coupling results in an enhanced interaction between individual localized plasmons at individual nanostructures [61] and thus an enhancement in the radiative efficiency increasing the spacer layer thickness moves the nanowires out of the evanescent field of the surface plasmon. A possible physical mechanism for the experimentally observed decay involves nonradiative decay of the excited states. The aluminum oxide deposited in these experiments was likely to be nonstoichio-metric, and defects in the oxide could act as recombination centers. Thicker oxides would result in higher areal densities of defects, and decay in fluorescence. A definitive assignment of the mechanism for the observed fall off of fluorescence would require determination of the complex dielectric function of our oxides (as deposited onto an Ag film), and inclusion in the field-square calculations. Finally it should be noted that at very small thicknesses quenching of the fluorescence is expected [38,62] consistent with observations of an optimum nanowire-substrate spacer thickness. 

In nonlinear programming (NLP) problems, either the objective function, the constraints, or both the objective and the constraints are nonlinear. Unlike LP, NLP solution does not always lie at the vertex of the feasible region. NLP optimum lies where the Jacobean of the function obtained by combining constraints with the objective function (using Lagrange multiphers as follows) is zero. The solution is local minimum if the Jacobian J is zero and the Hessian H is positive definite, and it is a local maximum if J is zero and H is negative definite. 

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