P M Pardolas

Bio: P M Pardolas is an academic researcher from University of Minnesota. The author has contributed to research in topics: Quadratic equation & Linear programming. The author has an hindex of 1, co-authored 1 publications receiving 99 citations.

Global minimization of large-scale constrained concave quadratic problems by separable programming

Abstract: The global minimization of a large-scale linearly constrained concave quadratic problem is considered. The concave quadratic part of the objective function is given in terms of the nonlinear variablesx ∈R n , while the linear part is in terms ofy ∈R k. For large-scale problems we may havek much larger thann. The original problem is reduced to an equivalent separable problem by solving a multiple-cost-row linear program with 2n cost rows. The solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum, and also gives a bound on the relative error in the function value of this incumbent. Ana priori bound on this relative error is obtained, which is shown to be ≤ 0.25, in important cases. If the incumbent is not a satisfactory approximation to the global minimum, a guaranteede-approximate solution is obtained by solving a single liner zero–one mixed integer programming problem. This integer problem is formulated by a simple piecewise-linear underestimation of the separable problem.

Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms

Abstract: Linearly constrained indefinite quadratic problems play an important role in global optimization. In this paper we study d.c. theory and its local approach to such problems. The new algorithm, CDA, efficiently produces local optima and sometimes produces global optima. We also propose a decomposition branch and bound method for globally solving these problems. Finally many numerical simulations are reported.

GloMIQO: Global mixed-integer quadratic optimizer

Abstract: This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$ -global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0.

Minimum concave-cost network flow problems: applications, complexity, and algorithms

Abstract: We discuss a wide range of results for minimum concave-cost network flow problems, including related applications, complexity issues, and solution techniques. Applications from production and inventory planning, and transportation and communication network design are discussed. New complexity results are proved which show that this problem is NP-hard for cases with cost functions other than fixed charge. An overview of solution techniques for this problem is presented, with some new results given regarding the implementation of a particular branch-and-bound approach.

An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds

Abstract: This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case ane-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.