On certain classes of variational inequalities and related iterative algorithms.
On computation of C-stationary points for equilibrium problems with linear complementarity constraints via homotopy method
In the paper we consider EPCCs with convex quadratic objective functions and one set of complementarity constraints. For this class of problems we propose a possible generalization of the homotopy method for finding stationary points of MPCCs. We analyze the difficulties which arise from this generalization. Numerical results illustrate the performance for randomly generated test problems.
On -preinvex-type functions.
On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On Orthogonal Linear ...1 Approximation.
On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method
For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.
On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball
We consider the non-convex quadratic maximization problem subject to the l1 unit ball constraint. The nature of the l1 norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.
On the Accuracy of Regularized Solutions to Quadratic Minimization Problems on a Half-Space, in Case of a Normally Solvable Operator
On the Ball Spanned by Balls.
On the closure of the sum of closed subspaces.
On the computer algebra implementation of the least squares method on the nonnegative orthant.
On the decrease of a quadratic function along the projected-gradient path.
On the minimum time problem in linear discrete systems with the discrete set of admissible controls
On the penalty approximation of quadratic programming problem
On the quadratic fractional optimization with a strictly convex quadratic constraint
In this paper, we have studied the problem of minimizing the ratio of two indefinite quadratic functions subject to a strictly convex quadratic constraint. First utilizing the relationship between fractional and parametric programming problems due to Dinkelbach, we reformulate the fractional problem as a univariate equation. To find the root of the univariate equation, the generalized Newton method is utilized that requires solving a nonconvex quadratic optimization problem at each iteration. A...
On the relationship between regression analysis and mathematical programming.
On the solution of a class of location problems. A sample problem
On Tridiagonal Linear Complementary Problems.
On Wellposedness Quadratic Function Minimization Problem on Intersection of Two Ellipsoids