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Primal-dual algorithm for weakly convex functions under sharpness conditions
Ewa Bednarczuk, The Hung Tran, Monika Syga
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap…
On duality for nonconvex minimization problems within the framework of abstract convexity
Ewa M. Bednarczuk, Monika Syga
By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The m…
Lagrangian duality for nonconvex optimization problems with abstract convex functions
Ewa M. Bednarczuk, Monika Syga
We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the -convexity theory and minimax theorem for -convex functions. We provide conditio…
On global properties of lower semicontinuous quadratically minorized functions
Monika Syga
We use the framework of a type of abstract convexity (-convexity) to investigate properties of lower semicontinuous quadratically minorized functions in Hilbert spaces. A…