scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

Newton's method associated to the interior point method for optimal reactive dispatch problem

2004 ◽  
Author(s):  
E.A. Belati ◽  
V.A. de Sousa ◽  
L.C.T. Nunes ◽  
G.R.M. da Costa
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Point Method

An Interior Point Method for Linear Programming Using Weighted Analytic Centers

2009 ◽  
Vol 41 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Julianne Anderson ◽  
Shafiu Jibrin
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Analytic Centers

3D magnetic sparse inversion using an interior-point method

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. J15-J32 ◽  
Author(s):  
Zelin Li ◽  
Changli Yao ◽  
Yuanman Zheng ◽  
Junheng Wang ◽  
Yuwen Zhang
Keyword(s):  
Objective Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Upper And Lower Bounds ◽  
Magnetic Data ◽  
Feasible Region ◽  
Bound Constraints ◽  
Susceptibility Model ◽  
Sparse Inversion

Rock susceptibility measurements are sometimes taken on outcrop and borehole rocks, and they provide valuable information for constraining magnetic data inversion. We have developed two approaches for 3D magnetic sparse inversion that effectively take advantage of the rock susceptibility information. Both approaches minimize a total objective function subject to bound constraints using an interior-point method. The first approach directly minimizes an [Formula: see text]-norm of the susceptibility model by keeping the bounds positive, in which case the objective function is differentiable in the feasible region. The second approach minimizes a more generalized [Formula: see text]-like-norm ([Formula: see text]) of the susceptibility model by approximating the [Formula: see text]-like-norm inversion as an iteratively reweighted least-squares problem. Moreover, this approach allows the model values to be either positive or negative. We also revealed the equivalence of our approaches and the binary inversion. The recovered models of both approaches are characterized by sharp boundaries. However, the credibility of recovered boundaries depends on the accuracy and validity of the user-specified upper and lower bounds. Our approaches are tested on the synthetic data and field data acquired over a copper-nickel deposit.

scholarly journals A Gradient-Based Interior-Point Method to Solve the Many-to-Many Assignment Problems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Nitish Das ◽  
P. Aruna Priya
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Accurate Solution ◽  
Point Method ◽  
Practical Implementation ◽  
Cardinality Constraint ◽  
Gradient Based ◽  
The Many ◽  
Logarithmic Barrier

The many-to-many assignment problem (MMAP) is a recent topic of study in the field of combinatorial optimization. In this paper, a gradient-based interior-point method is proposed to solve MMAP. It is a deterministic method which assures an optimal solution. In this approach, the relaxation of the constraints is performed initially using the cardinality constraint detection operation. Then, the logarithmic barrier function (LBF) based gradient descent approach is executed to reach an accurate solution. Experiments have been performed to validate the practical implementation of the proposed algorithm. It also illustrates a significant improvement in convergence speed for the large MMAPs (i.e., if group size, α≥80) over state-of-the-art literature.

scholarly journals A parallel primal–dual interior-point method for semidefinite programs using positive definite matrix completion

2006 ◽  
Vol 32 (1) ◽  
pp. 24-43 ◽  
Author(s):  
Kazuhide Nakata ◽  
Makoto Yamashita ◽  
Katsuki Fujisawa ◽  
Masakazu Kojima
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Matrix Completion ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Point Method ◽  
Semidefinite Programs ◽  
Primal Dual

scholarly journals A numerical feasible interior point method for linear semidefinite programs

2007 ◽  
Vol 41 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Djamel Benterki ◽  
Jean-Pierre Crouzeix ◽  
Bachir Merikhi
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Semidefinite Programs
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