•We introduce different types of tangent cones for convex vector SIO problems.•We introduce and compare four constraint qualifications (CQs).•We characterize (weakly, properly) efficient solutions in ...terms of cones.•KKT results are provided.
Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.
► We characterize different types of efficient points of linear VSIO problems. ► Characterizations in terms of cones involving the data and KKT conditions. ► Methodology based on identifying tangent ...cones at feasible points. ► Tangent cones only computable under (global or local) constraint qualifications.
Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.
The feasible set M in general semi-infinite programming (GSIP) need not be closed. This fact is well known. We introduce a natural constraint qualification, called symmetric Mangasarian-Fromovitz ...constraint qualification (Sym-MFCQ). The Sym-MFCQ is a nontrivial extension of the well-known (extended) MFCQ for the special case of semi-infinite programming (SIP) and disjunctive programming. Under the Sym-MFCQ the closure M has an easy and also natural description. As a consequence, we get a description of the interior and boundary of M. The Sym-MFCQ is shown to be generic and stable under C1-perturbations of the defining functions. For the latter stability the consideration of the closure of M is essential. We introduce an appropriate notion of Karush-Kuhn-Tucker (KKT) points. We show that local minimizers are KKT points under the Sym-MFCQ. PUBLICATION ABSTRACT
We consider semi-infinite programming problems
depending on a finite dimensional parameter
. Provided that
is a strongly stable stationary point of
, there exists a locally unique and continuous ...stationary point mapping
. This defines the local critical value function
, where
denotes the objective function of
for a given parameter vector
. We show that
is the sum of a convex function and a smooth function. In particular, this excludes the appearance of negative kinks in the graph of
.
A fault-tolerant control scheme is proposed for a class of commensurate-order fractional nonlinear systems that consists of two fractional-order observers (hybrid scheme). The diagnosis of the faults ...is performed by means of a model-free fractional proportional integral reduced-order observer that uses the fractional algebraic observability property. A fractional dynamical controller obtained in a natural way from the dynamics of a fractional high-gain observer is designed, which is constructed from a fractional generalised observability canonical form; the controller performs output tracking, thus eliminating the effects of the faults. A stability analysis on the overall system demonstrates that the origin is Mittag-Leffler stable. The proposed methodology is assessed by means of simulations on the fractional models of the Van der Pol oscillator and a DC motor.
Fourteen Dorper × Pelibuey ram lambs (initial body weight BW = 37.4 ± 1.0 kg and age = 4.5 mo) were housed in individual pens during a 30-d feeding period, and then slaughtered to determine the ...effects of zilpaterol hydrochloride (ZH) supplementation on productive performance, carcass characteristics and wholesale cut yields. Lambs were assigned under a randomized complete block design (initial BW as blocking factor) to one of two dietary treatments: basal diet without (control) or with 10 mg daily of ZH/lamb. Lambs fed ZH had greater (P ≤ .04) final BW, average daily gain and dry matter intake, but similar (P = .24) feed efficiency compared with control lambs. Hot and cold carcass weight, dressing percentage, longissimus muscle area and leg perimeter were greater (P ≤ .05) for ZH-fed lambs than for control lambs. With exception of blood percentage which decreased (P < .01) with ZH, wholesale cut yields and non-carcass components were unaffected (P ≥ .12) by ZH supplementation. In conclusion, ZH can be used to improve growth rate and dressing percentage, but not to increase wholesale cut yields in feedlot finishing ram lambs.
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