for (approximately) solving a linear system with a positive-definite coefficient ma- trix. This is ..... Definition 1.4.4 (Free gradient and chopped gradient) At a pint x, the free gradient .... the use of the CG method to solve a reduced system of e
By utilizing new parametric linearization technique, we can derive the parametric ...... If UBs −LBs ≤ ϵ, then the algorithm stops, and ys is an ϵ-global optimal ...
presents a brief description of experiments on protein folding, Gaussian mixture
models, and bundle ..... [1] Scott Kirkpatrick, D. Gelatt Jr., and Mario P Vecchi.
Jul 11, 1984 - These tasks were also formulated as optimization problems where the .... Not logged in Google [Search Crawler] (3000811494) 66.249.66.151.
the difficult path and went for a masters degree (thesis option). The whole idea ..... Most traditional dual active-methods are restricted to strictly convex problems,.
Chapter 1. Introduction. Quadratic optimization constitutes one of the most ..... A set of test problems for our numerical experiments reported in Chapters 4, .... tinuation method for computing all solutions of a polynomial equation system .... The
We consider the general nonconvex quadratic programming problem and provide a series of convex positive semidefinite programs (or LMI relaxations) whose ...
â Advanced Analytics Devision, Operations Research and Management Science R&D, SAS Insti- tute Inc., 100 SAS Campus Drive, Cary, NC 27513, USA.
Apr 2, 2004 - The University of Edinburgh. Mayfield Road, Edinburgh EH9 3JZ ... function to express the investors preference for a positive deviation from the mean in ...... [4] A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods, MPS-S
There are two ways to solve a quadratic equation: the quadratic formula and by
factoring. There are advantages and disadvantages to each. In both cases, we ...
Mar 16, 2016 - solvers such as trust region method [10], [11] and sequential quadratic ... University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Nether- ...... [9] A. Yeredor and B. D. Moor, âOn homogeneous least-squares problems.
Hans Mittelmannâ. Jiming Peng â . September 17 ...... tion of Digital Systems: Theory and Techniques, M.A. Breuer Ed., vol(1),. Prentice-hall: Englewood Cliffs, ...
BarzilaiâBorwein (QRPABB) method for minimizing differentiable functions on closed convex sets. ... box-constrained quadratic programming. Projected BB ...
Key words: Nonconvex optimization, Geometric programming, Semidefi- nite programming ..... For a complete theory and many applications of. SOS methods ...
Aug 20, 2004 - Keywords: Parametric optimization; Sensitivity analysis; Quadratic opti- mization; Invariancy interval; Invariant support set; Interior point meth-.
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We present a bundle method for convex nondifferentiable minimization where the model is a piecewise quadratic convex approximation of the objective function.
The algorithm is implemented in a code PENNON. The ... tional constraints, that the above two problems are equivalent. However, ... Both mod- els lead .... integration point) and zeros otherwise. ..... nonconvex case, the Cholesky factorization in St
Feb 4, 2017 - The thesis was written under the guidance and with the help of my super- visor, Prof. Tamás Terlaky. His valuable advices and extended ...
Name___________________________________. Period____.
Date________________. Solving Quadratic Equations by Factoring. Solve each
equation by ...
Today, we continue our work with quadratic word problems by solving several ...
Create equation(s) that express the information given in the problem's scenario.
1. Solve quadratic equations by factoring. The factoring techniques you have
learned provide us with tools for solving equations that can be written in the form.
phase generates, being it a saddle point, local minimizer, or global minimizer ... R-local and blockwise R-local minimizers and develop their global optimality ... For certain nonconvex problems, a local minimum is always global or good enough. ... m
AbstractâWe study nonconvex distributed optimization in multiagent networks with time-varying (nonsymmetric) connec- t
Mar 7, 2011 - Keywords: nonconvex quadratic programming, global optimization, ... â Mathematics and Computer Science Division, Argonne National ... to calculate critical points that satisfy the Karush-Kuhn-Tucker (KKT) conditions with a good objective ... program with linear equality, nonnegativity, and complementarity ...
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Globally Solving Nonconvex Quadratic Programming Problems via Completely Positive Programming
Jieqiu Chen and Samuel Burer
Mathematics and Computer Science Division Preprint ANL/MCS-P1837-0211
Abstract Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of computational experiments comparing the new algorithm with existing codes on a diverse set of test instances, we demonstrate that the new algorithm is an attractive method for globally solving nonconvex QP. Keywords: nonconvex quadratic programming, global optimization, branch-and-bound, semidefinite programming, copositive programming, completely positive programming.
1
Introduction
We consider the problem of optimizing a general quadratic function subject to linear and bound constraints: 1 T x Hx + f T x 2 s.t. Ax ≤ b
