Level sets relaxation, epigraphical relaxation and conditioning in optimization

Sophie Guillaume (1) , Michel Volle (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

We provide formulas for the optimal solution set of various relaxed optimization problems. Such a set is also recaptured by using an appropriate notion of conditioning.

Keywords: Abstract convexity · Hull operators · Moreau conjugate · Regularization · Composite conjugate · Conditioning

Domains: Mathematics [math]; Optimization and Control [math.OC]

Sophie Guillaume, Michel Volle. Level sets relaxation, epigraphical relaxation and conditioning in optimization. Positivity, 2015, pp.10.1007/s11117-015-0327-7. ⟨10.1007/s11117-015-0327-7⟩. ⟨hal-01128309⟩