Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

Preprint English OPEN
Wu, Changzhi; Li, Chaojie; Gao, David Yang;
  • Subject: Mathematics - Optimization and Control | Computer Science - Numerical Analysis | Computer Science - Data Structures and Algorithms

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimizati... View more
  • References (37)
    37 references, page 1 of 4

    [1] J.M. Ball: Some open problems in elasticity. In Geometry, Mechanics, and Dynamics, pages 3-59, Springer, New York, 2002.

    [2] E. G. Birgin, C. A. Floudas and J.M. Martinez, Global minimization using an Augmented Lagrangian method with variable lower-level constraints, Math. Program., Ser. A (2010) 125:139- 162.

    [3] J. Gallier, The Schur complement and symmetric positive semidefinite (and definite) matrices,˜jean/schurcomp.pdf.

    [4] Gao, D.Y.: Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Kluwer Academic, Dordrecht (2000).

    [5] Gao, D.Y. (2007). Solutions and optimality to box constrained nonconvex minimization problems J. Indust. and Manage. Optim., 3(2), 293-304.

    [6] Gao, D.Y.: Canonical duality theory: unified understanding and generalized solutions for global optimization. Comput. Chem. 33, 1964-1972, (2009).

    [7] Gao, D.Y. and Ruan, N. (2010). Solutions to quadratic minimization problems with box and integer constraints, J. Global Optimization, 47:463484. DOI 10.1007/s10898-009-9469-0

    [8] Gao, D.Y., Ruan, N, and Pardalos, P.M. (2010). Canonical dual solutions to sum of fourth-order polynomials minimization problems with applications to sensor network localization, in Sensors: Theory, Algorithms and Applications, P.M. Pardalos, Y.Y. Ye, V. Boginski, and C. Commander (eds). Springer.

    [9] Gao, D.Y., Strang, G.: Geometric nonlinearity: Potential energy, complementary energy, and the gap function. Quart. Appl. Math. 47(3), 487-504 (1989).

    [10] A. Kaplan and R. Tichatschke, Proximal point methods and nonconvex optimization, J. Glob. Optim., 13, 389-406, 1998.

  • Metrics
    views in OpenAIRE
    views in local repository
    downloads in local repository
Share - Bookmark