We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data [Formula: see text], including [Formula: ...

Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant θ for using nonconvex nonsmooth regularizat...

Shape restricted smoothing splines receive growing attention, motivated by a wide range of important applications in science and engineering. In this paper, we consider smoothing splines subject to general linear dynamics and control constraints, and formulate them as finite-horizon constrained linear optimal control problems with unknown initial state and control. By exploring techniques from ...

Necessary conditions of optimality in the form of a weak maximum principle are derived for optimal control problems with mixed constraints. Such conditions differ from previous work since they hold when a certain convexity assumption is replaced by an “interiority” assumption. Notably the result holds for problems with possibly nonsmooth mixed constraints and with additional pointwise set contr...

We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical re...

Various iterative methods are available for the approximate solution of nonsmooth minimization problems. For a popular nonsmooth minimization problem arising in image processing the suitable application of three prototypical methods and their stability is discussed. The methods are compared experimentally with a focus on choice of stopping criteria, influence of rough initial data, step sizes a...

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of thousands of variables. In the paper [Haarala, Miettinen, Mäkelä, Optimization Methods and Software, 19, (2004), pp. 673–692] we have described an efficient method for large-scale nonsmooth optimization. In this paper, we introduce a new variant of this method and prove its global conve...

We investigate the coordination of groups of autonomous robots performing spatially-distributed sensing tasks. We present facility location functions from geometric optimization and study their differentiable properties. We then design distributed coordination algorithms and analyze them as nonsmooth gradient flows. The resulting control laws correspond to basic interaction behaviors between th...

We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weirtype dual problems for our nonsmo...

We consider a bilevel optimization approach for parameter learning in nonsmooth variational models. Existing approaches solve this problem by applying implicit differentiation to a sufficiently smooth approximation of the nondifferentiable lower level problem. We propose an alternative method based on differentiating the iterations of a nonlinear primal–dual algorithm. Our method computes exact...