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Characterisation of zero duality gap for optimization problems in spaces without linear structure

Author

Listed:
  • Ewa Bednarczuk

    (Polish Academy of Sciences
    Warsaw University of Technology)

  • Monika Syga

    (Warsaw University of Technology)

Abstract

We prove sufficient and necessary conditions ensuring zero Lagrangian duality gap for Lagrangians defined with help of general perturbation functions. This kind of Lagrangians include generalized and augmented Lagrangians. To this aim, we use the $$\Phi $$ Φ -convexity theory and we formulate our zero duality gap conditions in terms of elementary functions $$\varphi \in \Phi $$ φ ∈ Φ . The obtained results apply to optimization problems involving prox-bounded functions, DC functions, weakly convex functions and paraconvex functions as well as infinite-dimensional linear optimization problems, including Kantorovich duality which plays an important role in determining Wasserstein distance.

Suggested Citation

  • Ewa Bednarczuk & Monika Syga, 2025. "Characterisation of zero duality gap for optimization problems in spaces without linear structure," Journal of Global Optimization, Springer, vol. 92(1), pages 135-158, May.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:1:d:10.1007_s10898-025-01477-6
    DOI: 10.1007/s10898-025-01477-6
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