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...

This paper extends the Global Capacity ANnouncement procedure proposed in [5] along two directions. First, two new stopping criteria are considered. Second, annual losses are evaluated using representative days to approximate the injection duration curve. The extensions are validated on an updated model of a real-life system. The emphasis is on the situation in the Walloon region of Belgium con...

Huang’s data-driven technique of Empirical Mode Decomposition (EMD) is presented, and issues related to its effective implementation are discussed. A number of algorithmic variations, including new stopping criteria and an on-line version of the algorithm, are proposed. Numerical simulations are used for empirically assessing performance elements related to tone identification and separation. T...

A novel Swarm Intelligence method for best-fit search, Stochastic Diffusion Search, is presented capable of rapid location of the optimal solution in the search space. Population based search mechanisms employed by Swarm Intelligence methods can suffer lack of convergence resulting in ill defined stopping criteria and loss of the best solution. Conversely, as a result of its resource allocation...

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...

2 Software details 4 2.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 File overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Calling sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 The initial point . . . . . . . . . . ....

This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Num...

In evolutionary algorithms (EAs), the need to efficiently measure population diversity arises in a variety of contexts, including operator adaptation, algorithm stopping and re-starting criteria, and fitness sharing. In this paper we introduce a unified measure of population diversity and define its relationship to the most common phenotypic and genotypic diversity measures. We further demonstr...

Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of convergence is analyzed. Three of the new definitions given here do not involve the unknown root. Numerical experiments using adaptive arithmetic with multiple preci...