TY - JOUR
T1 - Analysis of conjugate points for constant tridiagonal Hesse matrices of a class of extremal problems
AU - Kawasaki, H.
N1 - Funding Information:
The author would like to thank the referees for their valuable comments and helpful suggestions. This research was partially supported by the Grant-in Aid for General Scientific Research form the Japan Society for the Promotion of Science 14340037.
PY - 2003/4
Y1 - 2003/4
N2 - The conjugate point is a global concept in the calculus of variations. It plays an important role in second-order optimality conditions. A conjugate point theory for a minimization problem of a smooth function with n variables was proposed in (H. Kawasaki (2000). Conjugate points for a nonlinear programming problem with constraints. J. Nonlinear Convex Anal., 1,287-293; H. Kawasaki (2001). A conjugate points theory for a nonlinear programming problem. SIAM J. Control Optim., 40, 54-63.). In those papers, we defined the Jacobi equation and (strict) conjugate points, and derived necessary and sufficient optimality conditions in terms of conjugate points. The aim of this article is to analyze conjugate points for tridiagonal Hesse matrices of a class of extremal problems. We present a variety of examples, which can be regarded as a finite-dimensional analogy to the classical shortest path problem on a surface.
AB - The conjugate point is a global concept in the calculus of variations. It plays an important role in second-order optimality conditions. A conjugate point theory for a minimization problem of a smooth function with n variables was proposed in (H. Kawasaki (2000). Conjugate points for a nonlinear programming problem with constraints. J. Nonlinear Convex Anal., 1,287-293; H. Kawasaki (2001). A conjugate points theory for a nonlinear programming problem. SIAM J. Control Optim., 40, 54-63.). In those papers, we defined the Jacobi equation and (strict) conjugate points, and derived necessary and sufficient optimality conditions in terms of conjugate points. The aim of this article is to analyze conjugate points for tridiagonal Hesse matrices of a class of extremal problems. We present a variety of examples, which can be regarded as a finite-dimensional analogy to the classical shortest path problem on a surface.
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U2 - 10.1080/1055678031000109554
DO - 10.1080/1055678031000109554
M3 - Article
AN - SCOPUS:0038487307
SN - 1055-6788
VL - 18
SP - 197
EP - 205
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 2
ER -