Adjoint-Based Predictor-Corrector Sequential Convex Programming for Parametric Nonlinear Optimization

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorit...

[1]  Jiří V. Outrata,et al.  Mathematical Programs with Equilibrium Constraints: Theory and Numerical Methods , 2006 .

[2]  Hans Bock,et al.  A Direct Multiple Shooting Method for Real-Time Optimization of Nonlinear DAE Processes , 2000 .

[3]  J. F. Bonnans,et al.  Local analysis of Newton-type methods for variational inequalities and nonlinear programming , 1994 .

[4]  Moritz Diehl,et al.  Loss of Superlinear Convergence for an SQP-Type Method with Conic Constraints , 2006, SIAM J. Optim..

[5]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[6]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..

[7]  Yang Wang,et al.  Code generation for receding horizon control , 2010, 2010 IEEE International Symposium on Computer-Aided Control System Design.

[8]  F. Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997 .

[9]  Pierre Apkarian,et al.  Robust control via sequential semidefinite programming , 2001, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  M. Diehl,et al.  Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations , 2000 .

[11]  Moritz Diehl,et al.  Towards a Computer Algebra System with Automatic Differentiation for use with Object-Oriented modelling languages , 2010, EOOLT.

[12]  Masao Fukushima,et al.  Successive Linearization Methods for Nonlinear Semidefinite Programs , 2005, Comput. Optim. Appl..

[13]  Wim Michiels,et al.  Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback , 2011, IEEE Transactions on Automatic Control.

[14]  Andreas Griewank,et al.  On the local convergence of adjoint Broyden methods , 2009, Math. Program..

[15]  Toshiyuki Ohtsuka,et al.  A continuation/GMRES method for fast computation of nonlinear receding horizon control , 2004, Autom..

[16]  Lorenz T. Biegler,et al.  Optimization approaches to nonlinear model predictive control , 1991 .

[17]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[18]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[19]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[20]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[21]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[22]  Diethard Klatte,et al.  Nonsmooth Equations in Optimization: "Regularity, Calculus, Methods And Applications" , 2006 .

[23]  Andrea Walther,et al.  An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization , 2010, Optim. Methods Softw..

[24]  Andreas Griewank,et al.  On constrained optimization by adjoint based quasi-Newton methods , 2002, Optim. Methods Softw..

[25]  P. Deuflhard.  Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms , 2011 .

[26]  Moritz Diehl,et al.  An approximation technique for robust nonlinear optimization , 2006, Math. Program..

[27]  P. Toint,et al.  Partitioned variable metric updates for large structured optimization problems , 1982 .

[28]  Wolfgang Marquardt,et al.  Model predictive control for online optimization of semi-batch reactors , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[29]  F. Jarre.  On an Approximation of the Hessian of the Lagrangian , 2003 .

[30]  M. Stingl,et al.  A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization , 2007 .

[31]  Lorenz T. Biegler,et al.  Efficient Solution of Dynamic Optimization and NMPC Problems , 2000 .

[32]  Hans Bock,et al.  Numerical methods for optimum experimental design in DAE systems , 2000 .

[33]  Roland W. Freund,et al.  A sensitivity analysis and a convergence result for a sequential semidefinite programming method , 2003 .

[34]  J. Frédéric Bonnans,et al.  Perturbation Analysis of Optimization Problems , 2000, Springer Series in Operations Research.

[35]  Héctor Ramírez Cabrera,et al.  A Global Algorithm for Nonlinear Semidefinite Programming , 2004, SIAM J. Optim..

[36]  Jacques Gauvin,et al.  Directional Behaviour of Optimal Solutions in Nonlinear Mathematical Programming , 1988, Math. Oper. Res..

[37]  R. Tyrrell Rockafellar,et al.  Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets , 1996, SIAM J. Optim..

[38]  Roland W. Freund,et al.  Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling , 2007, Math. Program..

[39]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[40]  MORITZ DIEHL,et al.  A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control , 2005, SIAM J. Control. Optim..

[41]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[42]  Klaus Schittkowski,et al.  Very large scale optimization by sequential convex programming , 2004, Optim. Methods Softw..

[43]  C. Fleury.  Sequential Convex Programming for Structural Optimization Problems , 1993 .

[44]  Victor M. Zavala,et al.  Real-Time Nonlinear Optimization as a Generalized Equation , 2010, SIAM J. Control. Optim..

[45]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[46]  Moritz Diehl,et al.  Real-Time Optimization for Large Scale Nonlinear Processes , 2001 .

[47]  Moritz Diehl,et al.  Local Convergence of Sequential Convex Programming for Nonconvex Optimization , 2010 .

[48]  Masao Fukushima,et al.  An SQP-type algorithm for nonlinear second-order cone programs , 2007, Optim. Lett..

[49]  R. Serban,et al.  CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS , 2005 .

[50]  Dinh Quoc Tran,et al.  Real-Time Sequential Convex Programming for Optimal Control Applications , 2009, HPSC.

[51]  John Hauser,et al.  On the stability of receding horizon control with a general terminal cost , 2005, IEEE Transactions on Automatic Control.

[52]  Shengtai Li,et al.  Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution , 2002, SIAM J. Sci. Comput..