This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that … Read more
In this paper, we present a new adaptive algorithm for defining the solution set of a multiobjective linear programming problem, where the decision variables are upper and lower bounded, using the direct support method. The principle particularitie of this method is the fact that it handles the bounds of variables such are they are initially … Read more
We present a new primal-dual algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Results of this algorithm when applied on a three-criteria real-world power plant optimization problem are reported, thereby illustrating the feasibility of … Read more
Suppose that for a given optimisation problem (which might be multicriteria problem or a single-criteron problem), an additional objective function is introduced. How does the the set of solutions, i.~e.\ the set of efficient points change when instead of the old problem the new multicriteria problem is considered? How does the set of properly efficient … Read more
We study the efficient outcome set $Y_E$ of a bi-criteria linear programming problem $(BP)$ and present a quite simple algorithm for generating all extreme points of $Y_E$. Application to optimization a scalar function $h(x)$ over the efficient set of $(BP)$ in case of $h$ which is a convex and dependent on the criteria is considered. … Read more
We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise … Read more
New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more
In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start … Read more
We describe a complete solution of the linear-quaratic control problem with the linear term in the objective function on a semiinfinite interval. This problem has important applications to calculation of Nesterov-Todd and other primal-dual directions in infinite-dimensional setting. Citation Technical report, University of Notre Dame, December, 2003 Article Download View Linear-quadratic control problem with a … Read more