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A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

Jason Hicken(hickej2***at***rpi.edu)
Alp Dener(denera***at***rpi.edu)

Abstract: We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed method selects the subspace solution that minimizes a quadratic-penalty function over a trust-region. Analysis of the method indicates the potential for fast asymptotic convergence near the solution, which is corroborated by numerical experiments. The results also demonstrate the effectiveness and efficiency of the method in the presence of nonconvexity. Overall, the iterative solver is a promising matrix-free linear-algebra kernel for inexact-Newton optimization algorithms and is well-suited to partial-differential-equation constrained optimization.

Keywords: constrained optimization, nonconvex programming, inexact Newton, matrix-free optimization, Krylov subspace methods, flexible preconditioning

Category 1: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Applications -- Science and Engineering (Multidisciplinary Design Optimization )

Citation: Report 2014-21, Scientific Computation Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180

Download: [PDF]

Entry Submitted: 10/08/2014
Entry Accepted: 10/08/2014
Entry Last Modified: 10/08/2014

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