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AbstractThe aim of this paper is to study optimality conditions for differentiable linearly constrained pseudoconvex programs. The stated results are based on new transversality conditions which can be used instead of complementarity ones. Necessary and sufficient optimality conditions are stated under suitable generalized convexity properties. Moreover, two different pairs of dual problems are proposed and weak and strong duality results proved. Finally, it is shown how transversality conditions can be applied to characterize optimality of convex quadratic problems and to efficiently solve a particular class of Max-Min problems

AbstractThe aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function in the form of $$\phi \left( c^Tx+c_0,\frac{d^Tx+d_0}{b^Tx+b_0}\right) $$

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or $$\bar{\phi }\left( \frac{\bar{c}^Ty+\bar{c}_0}{a^Ty+a_0}, \frac{d^Ty+d_0}{b^Ty+b_0}\right) $$



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. These problems arise in bicriteria programs, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. Theoretical results are proved and applied to propose a solution algorithm. Computational results are provided, comparing various splitting criteria.