This paper deals with maximization and minimization of quasiconvex functions in a finite dimensional setting. Firstly, some existence results on closed convex sets, possibly containing lines, are ...presented. This is given via a careful study of reduction to the boundary and/or extremality of the feasible set. Necessary or sufficient optimality conditions are derived in terms of radial epiderivatives. Then, the problem of minimizing quasiconvex functions are analyzed via asymptotic analysis. Finally, some attempts to define asymptotic functions under quasiconvexity are also outlined. Several examples illustrating the applicability of our results are shown.
Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is revisited in view of recent literature on the subject, establishing, in particular, new characterizations for ...the second case. This gives rise to a new class of quasiconvex problems having zero duality gap or closedness of images of vector mappings associated to those problems. Such conditions are described for the classes of linear fractional functions and that of quadratic ones. In addition, some applications to nonconvex quadratic optimization problems under a single inequality or equality constraint, are presented, providing new results for the fulfillment of zero duality gap or dual strong-duality.
Some production models in finance require infinite-dimensional commodity spaces, where efficiency is defined in terms of an ordering cone having possibly empty interior. Since weak efficiency is more ...tractable than efficiency from a mathematical point of view, this paper characterizes the equality between efficiency and weak efficiency in infinite-dimensional spaces without further assumptions, like closedness or free disposability. This is obtained as an application of our main result that characterizes the solutions to a unified vector optimization problem in terms of its scalarization. Standard models as efficiency, weak efficiency (defined in terms of quasi-relative interior), weak strict efficiency, strict efficiency, or strong solutions are carefully described. In addition, we exhibit two particular instances and compute the efficient and weak efficient solution set in Lebesgue spaces.
Endometriosis of the appendix is a very rare entity and commonly affects females in childbearing age. Clinical presentation might be confusing varying from asymptomatic to acute abdominal pain and ...often mimicks acute appendicitis or chronic pelvic pain. Diagnosis is generally made after pathological examination as operative findings are usually non-specific. This condition poses a diagnostic challenge to radiologists and surgeons altogether and we therefore report a case of a middle aged female who presented with both right lower quadrant and right lower back pain. Recent literature is reviewed and radiological findings discussed.
We first establish sufficient conditions ensuring strong duality for cone constrained nonconvex optimization problems under a generalized Slater-type condition. Such conditions allow us to cover ...situations where recent results cannot be applied. Afterwards, we provide a new complete characterization of strong duality for a problem with a single constraint: showing, in particular, that strong duality still holds without the standard Slater condition. This yields Lagrange multipliers characterizations of global optimality in case of (not necessarily convex) quadratic homogeneous functions after applying a generalized joint-range convexity result. Furthermore, a result which reduces a constrained minimization problem into one with a single constraint under generalized convexity assumptions, is also presented.
Given a closed convex set K in Rn; a vector function F:K×K arrow right Rm; a closed convex (not necessarily pointed) cone P(x) in Rm with non-empty interior, PP(x) ≠ Ø, various existence results to ...the problem find x∈K such that F(x,y)∉- int P(x) ∀ y ∈K under P(x)-convexity/lower semicontinuity of F(x,c) and pseudomonotonicity on F, are established. Moreover, under a stronger pseudomonotonicity assumption on F (which reduces to the previous one in case m=1), some characterizations of the non-emptiness of the solution set are given. Also, several alternative necessary and/or sufficient conditions for the solution set to be non-empty and compact are presented. However, the solution set fails to be convex in general. A sufficient condition to the solution set to be a singleton is also stated. The classical case P(x)=Rm+ is specially discussed by assuming semi-strict quasiconvexity. The results are then applied to vector variational inequalities and minimization problems. Our approach is based upon the computing of certain cones containing particular recession directions of K and F.
The Journal Neuropsychoanalysis: An Interdisciplinary Journal for Psychoanalysis and the Neurosciences celebrated its 25th anniversary in 2023. The celebration gathered old and current editors. The ...story of the Journal and of neuropsychoanalysis is told by those directly involved in the project at its different stages. This text is a collection of the reflections that editors and guests shared on celebrating this special anniversary.
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