Efficiency in uncertain variational control problems

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

“…Bazargan and Mohebi [17] proposed a new constraints qualification for convex optimization and Ghosh et al [18] applied the generalized Hukuhara and Frechet differences in the area of interval optimization. However, to enrich the concept of interval optimization, Treanta [19][20][21][22] introduced several concepts on the different branches of interval optimization field viz. constrained interval-valued optimization, interval-valued variational control, and saddle-point optimality problems.…”

Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty

“…Classical intervals have shown a wide range of abilities, such as addressing problems using optimization to avoid overestimation of the optimal range of values [10][11][12]. In addition, the study of the solutions of a linear system when the coefficients and the independent term are considered as intervals has received much attention in the interval community, since it appears in the control design of different physical systems [13][14][15][16][17]. Pursuing the same line, in 2014 Modal Interval Analysis (MIA) [5], was presented as an extension of classical interval analysis.…”

“…According to (17), this inclusion is obtained by minimizing an assessment criterion Tolerance(Y, Y ∧Ŷ) or Tolerance(Ŷ, Y ∨Ŷ) (29) Otherwise, if the requirement is that the estimated solutions are to be contained in the experimental dataset, i.e.,Ŷ = f * (Y 0 , P) ⊆ Y, we apply the *-semantic theorem to obtain…”

Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems

“…There are various approaches used to tackle the optimization problems with uncertainty, such as stochastic process [5], fuzzy set theory [6] and interval analysis [7]. Among them, the method of interval analysis is to express an uncertain variable as a real interval or an interval-valued function (IVF), which has been applied to many fields, such as, the models involving inexact linear programming problems [8], data envelopment analysis [9], optimal control [10], goal programming [11], minimax regret solutions [12] and multiperiod portfolio selection problems [13] etc. Up to now, we can find many works involving interval-valued optimization problems (IVOPs) (see [14,15]).…”