New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.

Constraint qualifications in convex vector semi-infinite optimization

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.

CIMBNC- Combination and interactions of three kinds of nanoclays structural modifiers, for the colored bio-nanocomposites optimization

Biopolymers do not have competitive prices, which has prevented their industrial exploitation on a global scale so far. In this context, Using nanoclays, improvements in certain biopolymer properties, mainly mechanical and thermal, have been achieved. However, research has been much less focused on changing optical properties through the incorporation of nanoclays. At the same time, current research has focused on obtaining nanopigments, by organic dyes adsoptions into different nanoclays in order to achieve sustainable colouring and high performance materials. By combining advances in these lines of research, biodegradable composites with optimal mechanical and optical properties can be obtained. The aim of this work is to find the optimal formulation of naturally sourced nanopigments, incorporate them into a biological origin epoxy resin, and obtain a significant improvement in their mechanical, and optical properties. We combine three structural modifiers in the nanopigment synthesis: surfactant, silane and mordant salt. The latter was selected in order to replicate the mordant textile dyeing with natural dyes. Using a Taguchi’s desing L8, we look for the effect of the presence of the modifiers, the pH acidification, and the interactions effect between the synthesis factors. Three natural dyes were selected: chlorophyll, beta-carotene, and beetroot extract. Furthermore we use two kinds of laminar nanoclays, differentiated by the ion exchange charge: montmorillonite, and hydrotalcite. Then the thermal, mechanical and colorimetric characterization of the bionanocomposite materials was carried out. The optimal conditions to obtain the best bionanocomposite materials are using acid pH, and modifying the nanoclays with mordant and surfactant.

Ziphodont crocodiles, Pristichampsus vorax (Troxell), new combination, from the Eocene of North America / Wann Langston, Jr. --.

v.33:no.16(1975)

Spatial distribution patterns of ascidians (Ascidiacea: Tunicata) in combination with information on bathymetry, oceanography, chlorophyll-a, and sea-ice on the continental shelves off the northern Antarctic Peninsula during POLARSTERN cruise ANT-XXIX/3

Ascidians (Ascidiacea: Tunicata) are sessile suspension feeders that represent dominant epifaunal components of the Southern Ocean shelf benthos and play a significant role in the pelagic-benthic coupling. Here, we report the results of a first study on the relationship between the distribution patterns of eight common and/or abundant (putative) ascidian species, and environmental drivers in the waters off the northern Antarctic Peninsula. During RV Polarstern cruise XXIX/3 (PS81) in January-March 2013, we used seabed imaging surveys along 28 photographic transects of 2 km length each at water depths from 70 to 770 m in three regions (northwestern Weddell Sea, southern Bransfield Strait and southern Drake Passage), differing in their general environmental setting, primarily oceanographic characteristics and sea-ice dynamics, to comparatively analyze the spatial patterns in the abundance of the selected ascidians, reliably to be identified in the photographs, at three nested spatial scales. At a regional (100-km) scale, the ascidian assemblages of the Weddell Sea differed significantly from those of the other two regions, whereas at an intermediate 10-km scale no such differences were detected among habitat types (bank, upper slope, slope, deep/canyon) on the shelf and at the shelf break within each region. These spatial patterns were superimposed by a marked small-scale (10-m) patchiness of ascidian distribution within the 2-km-long transects. Among the environmental variables considered in our study, a combination of water-mass characteristics, sea-ice dynamics (approximated by 5-year averages in sea-ice cover in the region of or surrounding the photographic stations), as well as the seabed ruggedness, was identified as explaining best the distribution patterns of the ascidians.

[Lecture notes on pure mathematics. Convex sets]

Includes bibliographies.

Comparison of California accident rates for single and double tractor-trailer combination trucks. Final report.

Federal Highway Administration, Washington, D.C.

Perceived importance of zones surrounding a vehicle and learning to use a convex mirror effectively. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Passenger vehicle, light truck and van convex mirror optimization and evaluation studies. Volume 1: convex mirror optimization. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Passenger vehicle, light truck and van convex mirror optimization and evaluation studies. Volume 2: evaluation of alternative mirror configurations. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

The modern English verb-adverb combination /

Includes bibliographical references (p.[7]-8)

Safety criteria for longer combination vehicles. Final report.

Federal Highway Administration, Office of Safety and Traffic Operations Research and Development, McLean, Va.

Color in everyday : a manual for lay students, artisans and artists on the principles of color combination and color arrangement, and their applications in dress, home, business, the theatre and community play /

"The book has grown out of a course of lectures on 'Color and its applications, based on a study of Museum originals' given at the Metropolitan Museum of Art under the auspices of New York University."--Introd.

A guide to the selection, combination, and cooking of foods /

Some recipes include wine or liquor as ingredients.