On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems

In this paper, we extend the notions of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(\Phi ,\rho )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi mathvariant="italic">ρ</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>-invexity and generalized <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$(\Phi ,\rho )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi mathvariant="italic">ρ</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>-invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$(\Phi ,\rho )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi mathvariant="italic">ρ</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>-invexity. Copyright The Author(s) 2014