On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.     

On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Invex-convexlike functions and duality

We define a class of invex-convexlike functions, which contains all convex, pseudoconvex, invex, and convexlike functions, and prove that the Kuhn-Tucker sufficient optimality condition and the Wolfe duality hold for problems involving such functions. Applications in control theory are given.The author is grateful to Professor W. Stadler and the referees for many valuable remarks and suggestions, which have enabled him to improve considerably the paper.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Estimation of radon and thoron caused dose at exraction and processing sites of mineral sand mining area in Vietnam (HA TINH province)

Mineral sands are mined in several countries to supply to the titanium and zircon producing industries. Coastal black mineral sands usually contain, besides ilmenite (FeTiO₃) and rutile (TiO₂), radioactive minerals such as zircon (ZrSiO₄) and monazite (RePO₄). Radon and thoron activity concentration originated from natural radioactive contents of the black mineral sand was monitored at the extraction and processing for black minerals in the coastal areas of Ha Tinh Province, one of the around 40 coastal mineral sand deposits in Vietnam. The survey was carried out with the Raduet chambers made by Radosys Ltd—Hungary. The obtained results for 25 investigated points show that the measured values are not high in the residential houses and in case of the sand extraction site as well. At the titanium processing plant the measured values were higher than outside the facility (Radon: 18–55 Bq/m³ with average of 34 Bq/³ and Thoron 33–118 Bq/m³ with average of 58 Bq/m³) but still comparable to the average concentration of the world published by UNSCEAR. The typical outdoor levels of radon and thoron gas are each of the order of 10 Bq/m³. Although the radon concentrations were low in the zircon and titanium processing plants, the thoron concentrations in the houses for separating rutile and zircon were very high. At zircon processing factory, the thoron concentration could reach 2,931 Bq/m³ and the estimated annual effective dose would be 21.4 mSv/a. Intervention has to be taken in order to reduce the thoron level in this factory since the level of thoron and its progenies corresponding to an annual occupational effective dose is beyond the action level of 6 mSv/a.