One-Dimensional global optimization for observations with noise

Visualization of multi-objective decisions for the optimal design of a pressure swing adsorption system

“…On the other pole are problems where information about properties of the objective functions is very scarce, and their derivatives are not available. Especially difficult are problems with "noisy" objective functions [11], the values of which are e.g., computed by Monte Carlo methods. In such so called blackbox optimization case, methods based on statistical models of objective functions seem most appropriate [12].…”

Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems

“…The one-step optimality criterion prevails in the development of optimal algorithms of global optimization, see e.g. [2,8,11,18,19,23]. The concept of worst-case optimality, which is a standard in the theory of algorithms [1], is implemented e.g.…”

Global optimization for structured low rank approximation

“…Although the objective functions are often Lipschitz-continuous (see, e. g., [7,10,16,17,19]), it has very high Lipschitz constants which increase with N, the number of observations. Adding noise to the observed data increases the complexity of the objective function (see, e. g., [3,20]) and moves the global minimizer away from the vector of true parameters. Thus, efficient global optimization techniques should be used to tackle the stated problem.…”