‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

We propose a fast first-order method to solve multi-term nonsmooth composite convex minimization problems by employing a recent proximal average approximation technique and a novel adaptive parameter tuning technique. Thanks to this powerful parameter tuning technique, the proximal gradient step can be performed with a much larger stepsize in the algorithm implementation compared with the prior...

We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing an auxiliary variable, we utilize the proximal operator of the nonsmooth regularizer to transform the associated augmented Lagrangian into a function that i...

We extend the concept of bundle methods to address non-convex and nonsmooth optimization problems arising in the design of a feedback control law for the longitudinal flight control of a civil aircraft. Our novel approach has two advantages. It allows to handle the specific structure of the control law directly, and we can express control law specifications directly as band-limited frequency-do...

The session will focus on the recent developments in the theory of nonlinear evolution equations, optimal control theory and related topics including real life problems of mechanics, biology, economics, and medicine. The main topics of the session include, but are not limited to, analysis of solutions of evolution problems and partial differential equations, operator inclusions, evolution inclu...

We discuss in this paper a class of nonsmooth functions which can be represented, in a neighborhood of a considered point, as a composition of a positively homogeneous convex function and a smooth mapping which maps the considered point into the null vector. We argue that this is a sufficiently rich class of functions and that such functions have various properties useful for purposes of optimi...

We analyze distributed optimization algorithms where parts of data and variables are distributed over several machines and synchronization occurs asynchronously. We prove convergence for the general case of a nonconvex objective plus a convex and possibly nonsmooth penalty. We demonstrate two challenging applications, `1-regularized logistic regression and reconstruction ICA, and present experi...