Weak minimization and duality
Terence Weir, B. Mond, B. D. Craven · Numerical Functional Analysis and Optimization · 1987
Sufficient and necessary optimality conditions are given for weakly minimized optimization problems in terms of a vector valued Lagrangian. Lagrangian and Wolfe type duals are constructed and duality established using an ordering that accords with the definition of a weak minimum. The results for differentiable problems continue to hold under weakened convexity assumptions and for problems which quasiminimize rather than minimize.