论文信息 - Global Optimization of Homogeneous Polynomials on the Simplex and on the Sphere - 字舞流文

Global Optimization of Homogeneous Polynomials on the Simplex and on the Sphere

We obtain rigorous estimates for linear and semidefinite relaxations of global optimization problems on the simplex and on the sphere

[1] Aharon Ben-Tal,et al. Lectures on modern convex optimization , 1987 .

[2] B. Reznick. Sums of Even Powers of Real Linear Forms , 1992 .

[3] Yurii Nesterov,et al. Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[4] B. Reznick. Uniform denominators in Hilbert's seventeenth problem , 1995 .

[5] Melvyn B. Nathanson,et al. Additive Number Theory , 1996 .

[6] Panos M. Pardalos,et al. Interior Point Methods for Global Optimization , 1996 .

[7] P. Pardalos,et al. Interior Point Methods for Combinatorial Optimization , 1998 .

[8] P. Pardalos,et al. Handbook of Combinatorial Optimization , 1998 .

[9] Yurii Nesterov. Global quadratic optimization on the sets with simplex structure , 1999 .

[10] Arkadi Nemirovski,et al. Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[11] B. Reznick,et al. A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra , 2001 .

[12] Jean B. Lasserre,et al. Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[13] L. Faybusovich. On Nesterov's Approach to Semi-infinite Programming , 2002 .

[14] Etienne de Klerk,et al. Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming , 2002, J. Glob. Optim..