Global lower bounds for the VLSI macrocell floorplanning problem using semidefinite optimization

2005 ◽  
Author(s):  
P.L. Takouda ◽  
M.F. Anjos ◽  
A. Vannelli
Keyword(s):  
Lower Bounds ◽  
Semidefinite Optimization

scholarly journals Semidefinite Optimization Providing Guaranteed Bounds on Linear Functionals of Solutions of Linear Integral Equations with Smooth Kernels

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guangming Zhou ◽  
Chao Deng ◽  
Kun Wu
Keyword(s):  
Integral Equations ◽  
Lower Bounds ◽  
Semidefinite Optimization ◽  
Upper And Lower Bounds ◽  
Optimization Approach ◽  
Linear Functionals ◽  
Smooth Kernels ◽  
Smooth Kernel ◽  
Linear Integral ◽  
Linear Integral Equations

Based on recent progress on moment problems, semidefinite optimization approach is proposed for estimating upper and lower bounds on linear functionals defined on solutions of linear integral equations with smooth kernels. The approach is also suitable for linear integrodifferential equations with smooth kernels. Firstly, the primal problem with smooth kernel is converted to a series of approximative problems with Taylor polynomials obtained by expanding the smooth kernel. Secondly, two semidefinite programs (SDPs) are constructed for every approximative problem. Thirdly, upper and lower bounds on related functionals are gotten by applying SeDuMi 1.1R3 to solve the two SDPs. Finally, upper and lower bounds series obtained by solving two SDPs, respectively infinitely approach the exact value of discussed functional as approximative order of the smooth kernel increases. Numerical results show that the proposed approach is effective for the discussed problems.

Semidefinite Optimization Estimating Bounds on Linear Functionals Defined on Solutions of Linear ODEs

2016 ◽  
Vol 8 (4) ◽  
pp. 599-615
Author(s):  
Guangming Zhou ◽  
Chao Deng ◽  
Kun Wu
Keyword(s):  
Lower Bounds ◽  
Optimization Method ◽  
Semidefinite Optimization ◽  
Upper And Lower Bounds ◽  
Linear Functionals ◽  
Linear Ordinary Differential Equations ◽  
Estimation Problems ◽  
Smooth Coefficients ◽  
Taylor Polynomials ◽  
Linear Odes

AbstractIn this paper, semidefinite optimization method is proposed to estimate bounds on linear functionals defined on solutions of linear ordinary differential equations (ODEs) with smooth coefficients. The method can get upper and lower bounds by solving two semidefinite programs, not solving ODEs directly. Its convergence theorem is proved. The theorem shows that the upper and lower bounds series of linear functionals discussed can approach their exact values infinitely. Numerical results show that the method is effective for the estimation problems discussed. In addition, in order to reduce calculation amount, Cheybeshev polynomials are applied to replace Taylor polynomials of smooth coefficients in computing process.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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