论文信息 - Pathways to the optimal set in linear programming

Pathways to the optimal set in linear programming

This chapter presents continuous paths leading to the set of optimal solutions of a linear programming problem. These paths are derived from the weighted logarithmic barrier function. The defining equations are bilinear and have some nice primal-dual symmetry properties. Extensions to the general linear complementarity problem are indicated.

N. Megiddo

[1] George B. Dantzig,et al. Linear programming and extensions , 1965 .

[2] C. E. Lemke,et al. Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[3] Herbert E. Scarf,et al. The Approximation of Fixed Points of a Continuous Mapping , 1967 .

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

[5] G. Dantzig,et al. COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[6] Herbert E. Scarf,et al. The Solution of Systems of Piecewise Linear Equations , 1976, Math. Oper. Res..

[7] Robert L. Hemminger,et al. On 3-skein isomorphisms of graphs , 1982, Comb..

[8] R. Kellogg,et al. Pathways to solutions, fixed points, and equilibria , 1983 .

[9] O. Mangasarian. Normal solutions of linear programs , 1984 .

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

[11] Katta G. Murty,et al. A new interior variant of the gradient projection method for linear programming , 1985 .

[12] Michael A. Saunders,et al. On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method , 1986, Math. Program..

[13] Nimrod Megiddo,et al. Boundary Behavior of Interior Point Algorithms in Linear Programming , 1989, Math. Oper. Res..

[14] D. Bayer,et al. The Non-Linear Geometry of Linear Pro-gramming I: A?ne and projective scaling trajectories , 1989 .