Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

KT-invexity in optimal control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Convexidade generalizada em problemas de controle ótimo com tempo livre

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Condições de otimalidade para controle ótimo via formalismo de Dubovitskii-Milyutin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

First Order Characterizations of Pseudoconvex Functions

First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.

Calcification and ossification of the convexity of the falx cerebri and related subdural space in human cadavers

OBJECTIVE: The present work was planned to report the incidence of calcification and ossification of an isolated cranial dural fold. The form, degree of severity and range of extension of such changes will be described. Involvement of the neighboring brain tissue and blood vessels, whether meningeal or cerebral, will also be determined. The results of this study might highlight the occasional incidence of intracranial calcification and ossification in images of the head and their interpretation, by radiologists and neurologists, to be of dural or vascular origin.

METHODS: Two human formalin-fixed cadavers, one middle-aged female another older male, were investigated at the Anatomy Laboratory, College of Medicine, King Faisal University, Dammam, Kingdom of Saudi Arabia during the period from 2000 to 2003. In each cadaver, the skullcap was removed and the convexity of the cranial dura mater, as well as the individual dural folds, were carefully examined for any calcification or ossification. The meningeal and cerebral blood vessels together with the underlying brain were grossly inspected for such structural changes. Calcified or ossified tissues, when identified, were subjected to histological examination to confirm their construction.

RESULTS: The female cadaver showed a calcified parietal emissary vein piercing the skullcap and projecting into the scalp. The latter looked paler and deficient in hair on its right side. The base of the stump was surrounded by a granular patch of calcification. The upper convex border of the falx cerebri was hardened and it presented granules, plaques and a cauliflower mass, which all proved to be osseous in structure. The meningeal and right cerebral vessels were mottled with calcium granules. The underlying temporal and parietal lobes of the right cerebral hemisphere were degenerated. The male cadaver also revealed a calcified upper border of the falx cerebri and superior sagittal sinus. Osseous granules and plaques, similar to those of the first specimen, were also identified but without gross changes in the underlying brain.

CONCLUSION: Calcification or ossification of an isolated site of the cranial dura mater and the intracranial blood vessels might occur. These changes should be kept in mind while interpreting images of the skull and brain. Clinical assessment and laboratory investigations are required to determine whether these changes are idiopathic, traumatic, or as a manifestation of a generalized disease such as hyperparathyroidism, vitamin D-intoxication, or chronic renal failure.

A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

A generalized Drucker–Prager viscoplastic yield surface model for asphalt concrete

A generalized Drucker–Prager (GD–P) viscoplastic yield surface model was developed and validated for asphalt concrete. The GD–P model was formulated based on fabric tensor modified stresses to consider the material inherent anisotropy. A smooth and convex octahedral yield surface function was developed in the GD–P model to characterize the full range of the internal friction angles from 0° to 90°. In contrast, the existing Extended Drucker–Prager (ED–P) was demonstrated to be applicable only for a material that has an internal friction angle less than 22°. Laboratory tests were performed to evaluate the anisotropic effect and to validate the GD–P model. Results indicated that (1) the yield stresses of an isotropic yield surface model are greater in compression and less in extension than that of an anisotropic model, which can result in an under-prediction of the viscoplastic deformation; and (2) the yield stresses predicted by the GD–P model matched well with the experimental results of the octahedral shear strength tests at different normal and confining stresses. By contrast, the ED–P model over-predicted the octahedral yield stresses, which can lead to an under-prediction of the permanent deformation. In summary, the rutting depth of an asphalt pavement would be underestimated without considering anisotropy and convexity of the yield surface for asphalt concrete. The proposed GD–P model was demonstrated to be capable of overcoming these limitations of the existing yield surface models for the asphalt concrete.