Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a function with unfavorable properties like multimodality, invariants and non-differentiability. Recently various two-level optimization algorithms for multidimensional scaling with city-block distances have been proposed exploiting piecewise quadrati...

Title of dissertation: Adaptive Constraint Reduction for Convex Quadratic Programming and Training Support Vector Machines Jin Hyuk Jung, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dianne P. O’Leary Department of Computer Science Convex quadratic programming (CQP) is an optimization problem of minimizing a convex quadratic objective function subject to linear constraints. We...

The paper deals with a method for solving general convex quadratic programming problems with equality and inequality constraints. The interest in such problems comes from at least two facts. First, quadratic models are widely used in real-life applications. Second, in many algorithms for nonlinear programming, a search direction is determined at each iteration as a solution of a quadratic probl...

We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic constraints arising in the framework of Robust Convex Programming and demonstrate that these conditions are “tight” up to an absolute constant factor. We discuss applications in Control on the construction of a quadratic Lyapunov function for lin...

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem uncertain data in the constraints. We first introduce SOCP dual polytopic sets. Then, obtain zero duality gap result between and its terms of new type characteristic cone constraint qualification. also construct norm-constrained sets corresponding them. Moreover, some numer...

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev’s inequality for scalar random variables. Two semidefinite programming formulations are presented, with a constructive proof based on convex optimization duality and elementary...