Constrained Convex Programming Research Articles

Theoretical framework for the analysis of linearly constrained convex programs

Theoretical framework for the analysis of linearly constrained convex programs

Theoretical framework for the analysis of linearly constrained convex programs

A particularly convenient mathematical formulation for the modelling of a wide range of problems associated with operations research is a linearly constrained convex mathematical program. The paper analyses such a formulation using the notions of conjugate function theory. The aims of the analysis are easier computational possibilities and an enhanced understanding of the problem. To this end the duality theory of generalized geometric programming is specifically invoked. Application of this approach is made to three representative application areas: networks, resource allocation and entropy modelling.

An iterative row-action method for interval convex programming

The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form minf(x), subject to γ≤Ax≤δ, is proposed. For a certain family of functionsf(x), which includes the norm ∥x∥ and thex logx entropy function, convergence is proved. The present row-action method is particularly suitable for handling problems in which the matrixA is large (or huge) and sparse.

Some Algorithmic Aspects of the Theory of Optimal Designs

The approximate optimal design problem is treated as a constrained convex programming problem. A general class of optimal design algorithms is proposed from this point of view. Asymptotic convergence to optimal designs is also proved. Related problems like the implementability problem for the infinite support case and the general step-length algorithms are discussed.