An Interior Method for Nonconvex Semidefinite Programs

[1]  F. Jarre An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices , 1993 .

[2]  K. Goh,et al.  Control system synthesis via bilinear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[3]  R. Tapia,et al.  On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming , 2002 .

[4]  Carsten W. Scherer,et al.  From mixed to multi-objective control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[5]  Stephen J. Wright,et al.  The role of linear objective functions in barrier methods , 1999, Math. Program..

[6]  Michael A. Saunders,et al.  A Practical Interior-Point Method for Convex Programming , 1995, SIAM J. Optim..

[7]  Robert J. Vanderbei,et al.  An Interior-Point Algorithm for Nonconvex Nonlinear Programming , 1999, Comput. Optim. Appl..

[8]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[9]  Yinyu Ye,et al.  A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization , 1998, Comput. Optim. Appl..

[10]  A. Tits,et al.  A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties , 1998 .

[11]  F. Jarre Optimal ellipsoidal approximations around the Analytic center , 1994 .

[12]  Michael L. Overton,et al.  A Primal-dual Interior Method for Nonconvex Nonlinear Programming , 1998 .

[13]  J. Zowe,et al.  A combination of the bundle approach and the trust region concept , 1988 .

[14]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[15]  Y. Nesterov Global quadratic optimization via conic relaxation , 1998 .

[16]  Danny C. Sorensen,et al.  On the use of directions of negative curvature in a modified newton method , 1979, Math. Program..

[17]  Stephen J. Wright On the convergence of the Newton/log-barrier method , 2001, Math. Program..

[18]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[19]  Richard H. Byrd,et al.  A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .

[20]  Richard H. Byrd,et al.  Approximate solution of the trust region problem by minimization over two-dimensional subspaces , 1988, Math. Program..

[21]  C. Scherer Multiobjective H/sub 2//H/sub /spl infin// control , 1995 .

[22]  Masakazu Kojima,et al.  Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem , 2001, Comput. Optim. Appl..

[23]  Lower bounds in multi-objective H/sub 2//H/sub /spl infin// problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[24]  Florian Jarre,et al.  Optimal Truss Design by Interior-Point Methods , 1998, SIAM J. Optim..

[25]  Michael L. Overton,et al.  Large-Scale Optimization of Eigenvalues , 1990, SIAM J. Optim..

[26]  G. Sonnevend An "analytical centre" for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming , 1986 .

[27]  F. Jarre,et al.  An interior-point method for multifractional programs with convex constraints , 1995 .

[28]  Richard A. Tapia,et al.  A trust region strategy for nonlinear equality constrained op-timization , 1984 .

[29]  G. Papavassilopoulos,et al.  Biaffine matrix inequality properties and computational methods , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[30]  H. Wolkowicz,et al.  SQ2P, Sequential Quadratic Constrained Quadratic Programming , 1998 .

[31]  A. Nemirovski,et al.  Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint , 2000 .

[32]  Roland W. Freund,et al.  An interior-point method for fractional programs with convex constraints , 1994, Math. Program..

[33]  Anders Forsgren,et al.  Primal-Dual Interior Methods for Nonconvex Nonlinear Programming , 1998, SIAM J. Optim..

[34]  Levent Tunçel,et al.  Generalization of Primal—Dual Interior-Point Methods to Convex Optimization Problems in Conic Form , 2001, Found. Comput. Math..

[35]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[36]  A. Kaplan,et al.  Proximal interior point approach in convex programming (ill-posed problems) * † , 1999 .

[37]  José Mario Martínez,et al.  A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization , 1991, SIAM J. Optim..

[38]  M. Dettori,et al.  Design and implementation of a gain scheduled controller for a compact disc player , 1999, 1999 European Control Conference (ECC).

[39]  M. Powell The use of Band Matrices for Second Derivative Approximations in Trust Region Algorithms , 1998 .

[40]  M. Overton,et al.  On the optimal design of columns against buckling , 1992 .

[41]  John E. Dennis,et al.  A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization , 1997, SIAM J. Optim..