Gordan-Type Alternative Theorems and Vector Optimization Revisited

DOI10.1007/978-3-642-21114-0_2zbMath1303.90094OpenAlexW80960731MaRDI QIDQ2905364

Fernando Flores-Bazán, Cristián Vera, Fabián Flores-Bazan

Publication date: 27 August 2012

Published in: Vector Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-21114-0_2

zbMATH Keywords

vector optimizationgeneralized convexityconesweakly efficient solutionsproperly efficient solutionsquasi-interior pointsFritz-John optimality conditionsGordan-type alternative theoremsquasi-relative interior points

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (9)

Nonlinear programming via König's maximum theorem ⋮ A theorem of the alternative with an arbitrary number of inequalities and quadratic programming ⋮ Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint ⋮ Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap ⋮ Fritz John necessary optimality conditions of the alternative-type ⋮ Second-order strong Karush/Kuhn-Tucker conditions for proper efficiencies in multiobjective optimization ⋮ Proper or weak efficiency via saddle point conditions in cone-constrained nonconvex vector optimization problems ⋮ Characterizing FJ and KKT Conditions in Nonconvex Mathematical Programming with Applications ⋮ Vector duality for convex vector optimization problems by means of the quasi-interior of the ordering cone

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