On a convolution operation obtained by adding level sets : classical and new results
On a general convergence for Broyden like update method.
On a method of optimization
On a numerical method to approximate the solutions to bicriteria problems using a spline function
On a Numerical Treatment for the Curve-Tracing of the Homotopy Method.
On a Second-Order Step-Size Algorithm
On an iterative method for unconstrained optimization
We present a local and a semi-local convergence analysis of an iterative method for approximating zeros of derivatives for solving univariate and unconstrained optimization problems. In the local case, the radius of convergence is obtained, whereas in the semi-local case, sufficient convergence criteria are presented. Numerical examples are also provided.
On approximation of multifunctions with respect to the Vietoris topology
On discrete control problems having a minmax type objective functional
On Duality for Nonsmooth Lipschitz Optimization Problems
On existence of solutions to degenerate nonlinear optimization problems
We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
On finding optimal parameters of an oscillatory model of handwriting
In this paper, we show how optimization methods can be used efficiently to determine the parameters of an oscillatory model of handwriting. Because these methods have to be used in real-time applications, this involves that the optimization problems must be rapidely solved. Hence, we developed an original heuristic algorithm, named FHA. This code was validated by comparing it (accuracy/CPU-times) with a multistart method based on Trust Region Reflective algorithm.
On generalized derivatives for vector optimization problems.
On generalized semicontinuity-preserving multifunctions
On Henrici's transformation in optimization
Henrici’s transformation is a generalization of Aitken’s -process to the vector case. It has been used for accelerating vector sequences. We use a modified version of Henrici’s transformation for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.
On iterative methods for linearly constrained entropy maximization
On maximizing a concave function subject to linear constraints by Newton's method
On necessary optimality conditions in a class of optimization problems
In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints , where is a closed set and is a set-valued map. No convexity requirements are imposed on . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.
On nonlinear variational inequalities.
On optimizing a maximin nonlinear function subject to replicated quasi-arborescence-like constraints.
In this paper we present the motivation for using the Truncated Newton method in an algorithm that maximises a non-linear function with additional maximin-like arguments subject to a network-like linear system of constraints. The special structure of the network (so-termed replicated quasi-arborescence) allows to introduce the new concept of independent superbasic sets and, then, using second-order information about the objective function without too much computer effort and storage.