Christakis Charalambous

Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.

A lower bound for the controlling parameters of the exact penalty functions

The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.

Non-linear minimax optimization as a sequence of least pth optimization with finite values of p

Following developments in non-linear least pth optimization by the authors it is possible to derive two new methods of non-linear minimax optimization. Unlike the Polya algorithm in which a sequenc...

Minimax optimization of recursive digital filters using recent minimax results

The purpose of this paper is to use some recent work by the author on nonlinear minimax optimization to derive an efficient algorithm for the minimax optimization problem. This is followed by the application of the algorithm to the problem of choosing the coefficients of a recursive digital filter to meet arbitrary design specifications on the magnitude or the group delay characteristics.

On conditions for optimality of the nonlinearl1 problem

The purpose of this paper is to present necessary and sufficient conditions for optimality in the nonlinearl1 problem. Furthermore, the relationship of thel1 problem and the Pietrzykowskis approach to solve the nonlinear programming problem is discussed in detail.

Unconstrained optimization based on homogeneous models

In this paper a generalized algorithm for unconstrained optimization based on homogeneous functions is presented. It is shown that this generalized algorithm reaches the minimum of a homogeneous function inn + 2 iterations and does not require finding the minimum on the one-dimensional search. The Jacobson and Oksman algorithm can be derived from this general algorithm.

A negative-positive barrier method for non-linear programming

A new approach to non-linear programming is presented. The original non-linear programming problem is formulated as a sequence of unconstrained optimization problems. It is shown that this sequence will converge to the non-linear programming optimum. The proposed negative-positive harrier function has certain advantages over the usual barrier and penalty function methods. In addition, by minor modification of the new unconstrained objective function it is possible from a single optimization to see if there exists a feasible region.