The paper considers balanced packing problem of a given family of circles into a larger circle of the minimal radius as a multiextremal nonlinear programming problem. We reduce the problem to unconstrained minimization problem of a nonsmooth function by means of nonsmooth penalty functions. We propose an efficient algorithm to search for local extrema and an algorithm for improvement of the low...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable met...

Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper, we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines the traditional c...

In this thesis, we focus on the Nonsmooth Boundary-valued ODEs, whose right-hand functions are parameterized by algebraic variables that solve the initial-valuedproblems and the nonsmooth equations. Based on the idea of the initial value tech-niques used in traditional ODEs, a smoothing Newton method originated from theQSZ method is applied to the nonmsmooth dynamic systems. Mos...

The contribution deals with timestepping schemes for nonsmooth dynamical systems. Traditionally, these schemes are locally of integration order one, both in smooth and nonsmooth periods. This is inefficient for applications with few events like circuit breakers, valve trains or slider-crank mechanisms. To improve the behavior during smooth episodes, we start activities twofold. First, we includ...

Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper, we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines the traditional c...

We employ a fuzzy optimality condition for the Fréchet subdifferential and some advanced techniques of variational analysis such as formulae subdifferentials an infinite family nonsmooth functions coderivative scalarization to investigate robust duality nonsmooth/nonconvex multiobjective optimization problem dealing with uncertain constraints in arbitrary Asplund spaces. establish necessary con...