Analysis of a Quadratic Programming Decomposition Algorithm

Analysis of a Quadratic Programming Decomposition Algorithm

We analyze a decomposition algorithm for minimizing a quadratic objective function, separable in x1 and x2, subject to the constraint that x1 and x2 are orthogonal vectors on the unit sphere. Our algorithm consists of a local step where we minimize the objective function in either variable separately, while enforcing the constraints, followed by a global step where we minimize over a subspace g...

Efficient Linear Discriminant Analysis Using a Fast Quadratic Programming Algorithm

An algorithm is proposed for performing linear discriminant analysis using a single-layered feedforward network. The algorithm follows successive steepest descent directions with respect to the perceptron cost function, taking care not to increase the number of misclassified patterns. The algorithm has no free parameters and therefore no heuristics are involved in its application. Its efficienc...

Large-scale decomposition for successive quadratic programming

Complex Matrix Decomposition and Quadratic Programming

This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In this paper it is shown that stronger results can be obtained for the complex Hermitian case. In part...

Quadratic bi-level programming problems: a fuzzy goal programming approach

This paper presents a fuzzy goal programming (FGP) methodology for solving bi-level quadratic programming (BLQP) problems. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vec...