An Enumeration Method of Various Optimal Truss Topologies using Optimal Solution by the Interior Point Method

2014 ◽  
Author(s):  
T. Takada
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method

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.

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 Primal-Dual Interior-Point Method for Facility Layout Problem with Relative-Positioning Constraints

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 60
Author(s):  
Shunichi Ohmori ◽  
Kazuho Yoshimoto
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Facility Layout ◽  
Optimal Solution ◽  
Point Method ◽  
Interior Point Algorithm ◽  
Relative Positioning ◽  
Layout Problem ◽  
Facility Layout Problem ◽  
Primal Dual

We consider the facility layout problem (FLP) in which we find the arrangements of departments with the smallest material handling cost that can be expressed as the product of distance times flows between departments. It is known that FLP can be formulated as a linear programming problem if the relative positioning of departments is specified, and, thus, can be solved to optimality. In this paper, we describe a custom interior-point algorithm for solving FLP with relative positioning constraints (FLPRC) that is much faster than the standard methods used in the general-purpose solver. We build a compact formation of FLPRC and its duals, which enables us to establish the optimal condition very quickly. We use this optimality condition to implement the primal-dual interior-point method with an efficient Newton step computation that exploit special structure of a Hessian. We confirm effectiveness of our proposed model through applications to several well-known benchmark data sets. Our algorithm shows much faster speed for finding the optimal solution.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

scholarly journals An interior point method for isogeometric contact

2014 ◽  
Vol 276 ◽  
pp. 589-611 ◽  
Author(s):  
İ. Temizer ◽  
M.M. Abdalla ◽  
Z. Gürdal
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method

scholarly journals A tailored inexact interior-point method for systems analysis

2008 ◽  
Author(s):  
Janne Harju Johansson ◽  
Anders Hansson
Keyword(s):  
Interior Point ◽  
Systems Analysis ◽  
Interior Point Method ◽  
Point Method

On a Nonlinear Multiple-Centralitycorrections Interior-Point Method for Optimal Power Flow

2001 ◽  
Vol 21 (5) ◽  
pp. 62-62 ◽  
Author(s):  
G. L. Torres ◽  
V. H. Quintana
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Point Method ◽  
Optimal Power
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