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.

Early Intermediate and Middle Horizon ceramic styles of the Cuzco Valley / Brian S. Bauer, Bradford M. Jones.

n.s. no.34(2003)

A Roadmap for Strengthening International Collaboration in Research and Innovation under Horizon 2020. EU Center Singapore Background Brief No. 9, May 2013

This  background  brief  looks  into  the  new  research  and  innovation  strategy  introduced  by  the  European  Union  embodied in the Horizon 2020 funding programme. It focuses  on the  prospect  for  international  collaboration  in  Horizon  2020, and presents a roadmap for both European institutions  and  those  from  key  third  countries  to  get  ready  for  the  opportunities provided by this funding instrument to embark  on interesting research and innovation. The brief begins by  outlining the efforts by the EU to address issues of economic  competitiveness with a new growth strategy Europe 2020 in  response to the enormous challenges faced by Europe in the  midst of the debt  crisis. It looks at the introduction of the  Innovation Union  as  a  Europe 2020  initiative,  and  explains  how the  new  financial  instrument,  Horizon  2020,  may  be  used to support the primary goals   of more jobs, improved  lives,  better  society  and  the  global  competitiveness  of  Europe.  The  brief  also  outlines  the  major  differences  of  Horizon 2020 from the previous framework programmes, and  recommends close collaboration between the European and  the key third countries. The brief also proposes general and  priority‐specific  strategies  for  national  research  councils,  universities  and  research  institution  to  get  ready  to  participate in the Horizon 2020 programme.  

Is Horizon 2020 really more SME-friendly? A look at the figures. CEPS Commentary, 17 February 2016

Small- and medium-sized enterprises (SMEs) play a key role in the EU economy.[1] According to the latest “SME performance review” published by the European Commission,[2] in 2014 there were 22 million SMEs active in the non-financial business sectors, generating more than €3.7 trillion in added value and employing approximately 90 million people. SMEs’ contribution to the European economy becomes even more apparent if one considers that 99 out of every 100 enterprises active in the EU non-financial economy are SMEs, and that these firms account for about 67% of the total employment and some 60% of the overall added value produced in Europe. Against this background, enhancing the competitiveness of European SMEs is essential in order to foster the competitiveness of the EU economy as a whole. And since the competitiveness of European SMEs in the global arena largely depends on their ability to innovate,[3] unlocking the innovation potential of SMEs becomes pivotal to fostering growth and jobs in Europe.

Beyond the horizon : using foresight to protect the environmental future /

Mode of access: Internet.

Pursuit of the horizon, a life of George Catlin, painter & recorder of the American Indian.

Mode of access: Internet.

The characteristic impedance of the fin antenna of infinite length /

"Contract No. AF33(616)-3220 Project No. 6(7-4600) Task 40572 Wright Air Development Center"

A study of the non-uniform convergence of the inverse of a doubly-infinite matrix associated with a boundary value problem in a waveguide /

"Contract AF33(616)-6079 Project No. 9-(13-6278), Task No. 40572. Sponsored by: Aeronautical Systems Division"

On the solution of a class of Wiener-Hopf integral equations in finite and infinite ranges /

"Sponsored by: Wright Air Development Center"

A blast-wave theory of crater formation in semi-infinite targets,

"Resaerch...sponsored by the National Aeronautics and Space Administration under Contract no. NAS 3-2121."

Acoustic radiation of a cylindrical bar and an infinite plate excited by the field of a ship propeller,

Photocopy.

Binns's justice : Digest of the laws and judicial decisions of Pennsylvania, touching the authority and duties of justices of the peace: including all the required forms of process, docket entries, and fee bills ... The whole law in relation to landlord and tenant; insolvent debtors; elections; and fees: the general enactments of the inspection laws; militia laws; and many other laws: with an infinite variety of law forms ... /

The Magistrate's vocabulary of law terms and law phrases: p. 41-61.

Back scattering of a plane electromagnetic wave from an infinite cylinder of plasma with small axial gradients and arbitrary radial gradients of electron density : normal incidence /

"Prepared under contract no. NOrd 18053."