This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kučera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems with Coulomb friction. Journal of Computational and Applied Mathematics, 164/165, 387–408.]. The propos...

In this paper, we study a nonconvex quadratic minimization problem with two constraints, one of which being convex. We introduce convex relaxations (CQRs) and discuss cases, where the is equivalent to exactly CQRs. Particularly, show that global optimal solution can be recovered from an Through equivalence, new conditions under enjoys strong Lagrangian duality, generalizing recent condition in ...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Integral Quadratic Constraints (IQC) are inequalities used to describe (partially) possible signal combinations within a given dynamical system. IQC offer a framework for abstracting ”challenging” (e.g. non-linear, time-varying, uncertain, or distributed) elements of dynamical system models to aid in rigorous analysis of robust stability and performance (more specifically, to establish L2 gain ...

support vector regression (svr) solves regression problems based on the concept of support vector machine (svm). in this paper, a new model of svr with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...

A collection of converse theorems for integral quadratic constraints (IQCs) is established linear time-invariant systems. It demonstrated that when a system interconnected in feedback with an arbitrary satisfying IQC stable, then the given must necessarily satisfy complementary IQC. These are specialized to derive multiple versions passivity results. They cover standard notions strict as well i...