ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.

On alternative theorems and necessary conditions for efficiency

In this paper, we establish theorems of the alternative for a system described by inequalities, equalities and an inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.Theorem of the alternative, Kuhn-Tucker necessary condition, constraint qualification.

On constraint qualifications with generalized convexity and optimality conditions

This paper deals with a multiobjective programming problem involving both equality constraints in infinite dimensional spaces. It is shown that some constraint qualifications together with a condition of interior points are sufficient conditions for the invexity of constraint maps with respect to the same scale map. Under a new constraint qualification which involves an invexity condition and a generalized Slater condition a Kuhn-Tucker necessary condition is established.Invexity, scale, constraint qualification, nearly S-convelike mapping.

Analysis of the Lagging Time of Employment Structure in Vietnam

If any country’s or region's employment structure lags behind the industrial structure adjustment, which shows that the two structures are not developing in coordination. However, the deviation degree of structure is mainly the imbalance between industrial structure and employment structure. The lag refers to the degree to which the employment structure lags behind the industrial structure in the time dimension, and when the relationship between industrial structure and employment structure is measured in terms of time. Employment lags behind time over a long horizon which in turn causes serious unemployment, and affect industrial structure adjustment and upgrade. The study construct an analysis model for the lag time of the employment structure and provide findings that will resolve the incompatible state of the two structures, and promote the healthy development of industrial structure and employment structure in Vietnam. Through the research conclusion it is revealed that, after three years, the effects of industrial structure adjustment fully reflected the change of employment structure in Vietnam. Keywords: Lagging Time; Employment Structure; Vietna

On necessary conditions for efficiency in directionally differentiable optimization problems

This paper deals with multiobjective programming problems with inequality, equality and set constraints involving Dini or Hadamard differentiable functions. A theorem of the alternative of Tucker type is established and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Directionally differentiable functions, Kunh-Tucker necessary conditions, Lagrange multipliers, theorem of the alternative.

Proposal of a Combined Environmental Management Solution for Municipal Solid Waste (MSW) Separation in a Developing Country: for Pilot Realization in Hanoi, Vietnam

Municipal solid waste (MSW), thousands of tons of which increasingly generated daily in human life by the rapid urbanization, population migration and industrialization not only in Vietnam, but in all developing countries are causing many serious problems in Environmental management for the authorities of these issues. In Vietnam, various approaches, solutions and programs were studied, suggested and deployed over the last decades, but the most of them have stopped at the level of pilot-programs and have generally not been replicable, so not been applied in wide scale. The most challenging issue of MSW management systems is non-applied or not fully - done waste separation practice at sources, caused by not only limited collection equipment, staff and working efficiency, but also lack of investment in infrastructure and limited public awareness. These circumstances raised the real need of a combined Environmental Management solution for municipal solid waste (MSW) separation at sources, especially in urban residential households. This paper proposes a combined management solution for municipal solid waste (MSW) separation at sources, based on applying and combining 4 main environmental management instruments: 1- Legislation, 2- Economic, 3- Analysis, assessment and technology, 4-  Education and Communication. A pilot realization in Hanoi, Vietnam is proposed with detail description of the solution and reasonable argumentation. The solution effectiveness, judged on the basis of the collected data is presented

Proposal of a Combined Environmental Management Solution for Municipal Solid Waste (MSW) Separation in a Developing Country: for Pilot Realization in Hanoi, Vietnam

Municipal solid waste (MSW), thousands of tons of which increasingly generated daily in human life by the rapid urbanization, population migration and industrialization not only in Vietnam, but in all developing countries are causing many serious problems in Environmental management for the authorities of these issues. In Vietnam, various approaches, solutions and programs were studied, suggested and deployed over the last decades, but the most of them have stopped at the level of pilot-programs and have generally not been replicable, so not been applied in wide scale. The most challenging issue of MSW management systems is non-applied or not fully - done waste separation practice at sources, caused by not only limited collection equipment, staff and working efficiency, but also lack of investment in infrastructure and limited public awareness. These circumstances raised the real need of a combined Environmental Management solution for municipal solid waste (MSW) separation at sources, especially in urban residential households. This paper proposes a combined management solution for municipal solid waste (MSW) separation at sources, based on applying and combining 4 main environmental management instruments: 1- Legislation, 2- Economic, 3- Analysis, assessment and technology, 4-  Education and Communication. A pilot realization in Hanoi, Vietnam is proposed with detail description of the solution and reasonable argumentation. The solution effectiveness, judged on the basis of the collected data is presented