Nonconvex variational problems related to a hyperbolic equation

We first prove a new Lyapunov-type theorem which will yield existence of solutions to nonconvex minimum problems involving some hyperbolic equations on rectangular domains with Darboux boundary conditions. Some problems with obstacle and bang-bang results are also considered

Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems

Motivated by many applications (for instance, some production models in finance require infinity-dimensional commodity spaces, and the preference is defined in terms of an ordering cone having possibly empty interior), this paper deals with a unified model, which involves preference relations that are not necessarily transitive or reflexive. Our study is carried out by means of saddle point conditions for the generalized Lagrangian associated with a cone-constrained nonconvex vector optimization problem. We establish a necessary and sufficient condition for the existence of a saddle point in case the multiplier vector related to the objective function belongs to the quasi-interior of the polar of the ordering set. Moreover, exploiting suitable Slater-type constraints qualifications involving the notion of quasi-relative interior, we obtain several results concerning the existence of a saddle point, which serve to get efficiency, weak efficiency and proper efficiency. Such results generalize, to the nonconvex vector case, existing conditions in the literature. As a by-product, we propose a notion of properly efficient solution for a vector optimization problem with explicit constraints. Applications to optimality conditions for vector optimization problems are provided with particular attention to bicriteria problems, where optimality conditions for efficiency, proper efficiency and weak efficiency are stated, both in a geometric form and by means of the level sets of the objective functions

Continued Dialogue on The Oxford-style Debate from the 15th Annual Congress of the International Neuropsychoanalysis Society, New York City, 2014: Speaking to the subject or speaking to the function: each address requires its proper terms

In neuropsychoanalysis, the epistemological line most held is the “dual aspect monism” perspective. This perspective holds that “our brains, including mind, are made of one kind of stuff, cells, but we perceive this stuff in two different ways” (Solms & Turnbull, 2003, pp. 56–58; our italics). One is the neuroscientists’ “objective” way, or the brain, which we dissect “with scalpel and microscope or look at it with brain scans and then trace neurochemical pathways.” The other way is the psychoanalysts’ “subjective” way, or the mind: “how we feel and what we think. Freud refined this kind of observation into free association.” As, however, there is only one object, in the end, there is a more or less direct correspondence between phenomena of the brain and phenomena of the mind.SCOPUS: no.jinfo:eu-repo/semantics/publishe

Speaking to the subject or speaking to the function: each address requires its proper terms: The Oxford-style debate: the 15th neuropsychoanalysis congress, New York, 2014

info:eu-repo/semantics/publishe