Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily finite. Their relationships with each other in connection with the best approximations are investigated. As appli...

Assume that there exists a hypersurface singularity which cannot be resolved by iterated monoidal transformations in positive characteristic. We show that in the set of defining functions of hypersurface singularities which cannot be resolved, we can find a function satisfying very strong conditions. By these conditions we may be able to deduce a contradiction under the above assumption. Beside...

We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration o...

This paper summarizes as a working paperbasic facts in both nite and in nite dimensional optimization in view of optimality conditions and stability of solutions to perturbed problems. Begining with section 4, partially new and unpublished results are included, elaborated in joint work with D. Klatte, Univ. Zuerich.

Introduction The first part of the paper presents several properties of saddle point matrices with two vector blocks. In these block matrices, the top-left block is a real square matrix , the topright block is the column vector with all entries , the bottom-left block is transposed, and the bottom-right block has the single entry . If is symmetric, the saddle point matrix can be interpreted as ...

We study optimal control problems of systems describing the flow of incompressible shear-thickening fluids. We prove existence of solutions and derive necessary optimality conditions under precise restrictions on the optimal control.

Development in interior point methods has suggested various solution trajectories, also called central paths, for linear programming. In this paper we define a new central path through a log-exponential perturbation to the complementarity equation in the Karush-Kuhn-Tucker system. The behavior of this central path is investigated and an algorithm is proposed. The algorithm can compute an -optim...

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...

This paper presents a new clustering algorithm ,which is based on fuzzy c-lines, can treat data with some errors. First, the tolerance is formulated and introduce into optimization problem of clustering. Next, the problem is solved using Karush-Kuhn-Tucker conditions. Last, the algorithm is constructed based on the results of solving the problem. Some numerical examples for the proposed method ...

This paper presents a parameterized family of equilibrium strategy profiles for three-player Kuhn poker. This family illustrates an important feature of three-player equilibrium profiles that is not present in two-player equilibrium profiles the ability of one player to transfer utility to a second player at the expense of the third player, while playing a strategy in the profile family. This f...