15h30 - 15h55
A New Primal-dual Operator Splitting Scheme and its Applications
In this talk, I will introduce a new primal-dual algorithm for minimizing f(x) + g(x) + h(Ax), where f, g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. This new algorithm has the Chambolle-Pock and many other algorithms as special cases. It also enjoys most advantages of existing algorithms for solving the same problem. Then I will show some applications including fused lasso, image processing, and decentralized consensus optimization.
15h55 - 16h20
Calculus for directional limiting normal cones and subgradients
In the recent years, directional versions of the limiting (Mordukhovich) normal cone, the coderivative of a multifunction, the metric subregularity, etc. have been intensively studied by Gfrerer, yielding very interesting results. In this talk we present some basic calculus rules for these limiting objects valid under mild assumptions. E.g. we provide (upper) estimates for the directional limiting normal cone of a constraint set, the directional limiting subdifferential of a composition of functions, the directional coderivative of a composition of multifunctions, etc. We conclude the talk by showing some applications of the proposed calculus.
16h20 - 16h45
A comparison of alternative c-conjugate dual problems in infinite convex optimization
In this work we obtain a Fenchel-Lagrange dual problem for an infinite dimensional optimization primal one, via pertubational approach and using a conjugation scheme called c-conjugation instead of the classical Fenchel conjugation. This scheme is based on the generalized convex conjugation theory. We analyze some inequalities between the optimal values of Fenchel, Lagrange and Fenchel-Lagrange dual problems and we establish sufficient conditions under which they are equal. Also we study the relations between the optimal solutions and the solvability of the three mentioned dual problems.