Continuity of the null space basis and constrained optimization

Generated the Integer Null Space and Conditions for Determination of an Integer Basis Using the ABS Algorithms

ON THE CONTINUITY OF PROJECTIONS AND A GENERALIZED GRAM-SCHMIDT PROCESS

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization Equality Constrained Quadratic Programming Problems Arising in Optimization

We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computin...

Constrained Multi-Objective Optimization Problems in Mechanical Engineering Design Using Bees Algorithm

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using classical optimization methods, this paper presents a Multi-Objective Bees Algorithm (MOBA) for solving the multi-objective optimal of mechanical engineering problems design. In the pre...

On the duality of quadratic minimization problems using pseudo inverses

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...