This paper presents a perturbation based search method to solve the unconstrained binary quadratic programming problem. The proposed algorithm was tested with some of the standard test problems and the results are reported for 10 instances of 50, 100, 250, & 500 variable problems. A comparison of the performance of the proposed algorithm with other heuristics and optimization software is made. ...

We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also extend the result to a noisy variant of gradient descent method, where exact...

Active-set quadratic programming (QP) methods use a working set to define the search direction and multiplier estimates. In the method proposed by Fletcher in 1971, and in several subsequent mathematically equivalent methods, the working set is chosen to control the inertia of the reduced Hessian, which is never permitted to have more than one nonpositive eigenvalue. (We call such methods inert...

A method for solving free boundary problems for journal bearings by means of finite differences has been proposed by Christopherson. We analyse Christopherson's method in detail for the case of an infinite journal bearing where the free boundary problem is as follows: Given T > 0 and h(t) find r E (0, T] and p(t) such that (i) [ffipj = h' for t G (0, r), (Ü) />(0) = 0, (iii) p(t) = 0 for t S [r...

Most panel method implementations use both low order basis function representations of the solution and flat panel representations of the body surface. Although several implementations of higher order panel methods exist, difficulties in robustly computing the self term integrals remain. In this paper, methods for integrating the single and double layer self term integrals are presented. The ap...

a r t i c l e i n f o Do congestion externalities offer a reason to depart from complete price stability as the only goal of monetary policy in a New Keynesian model featuring search frictions, and under what conditions is the welfare cost of labor-market distortions sizable? This paper tries to answer these questions by deriving a linear quadratic framework for optimal monetary policy analysis...

We present a general boosting method extending functional gradient boosting to optimize complex loss functions that are encountered in many machine learning problems. Our approach is based on optimization of quadratic upper bounds of the loss functions which allows us to present a rigorous convergence analysis of the algorithm. More importantly, this general framework enables us to use a standa...

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iterat...

Line search algorithms for nonlinear programming must include safeguards to enjoy global convergence properties. This paper describes an exact penalization approach that extends the class of problems that can be solved with line search SQP methods. In the new algorithm, the penalty parameter is adjusted at every iteration to ensure sufficient progress in linear feasibility and to promote accept...

Criteria containing a barrier function i.e., an unbounded function at the boundary of the feasible solution domain are frequently encountered in the optimization framework, in particular in interior point methods for constrained optimization. Barrier function has to be carefully handled in the optimization algorithm. When an iterative descent method is used for the minimization, a search along ...