A new full-NT step interior-point method for circular cone optimization

Kheirfam, Behrouz

doi:10.17535/crorr.2019.0023

Cited by 3 publications

(2 citation statements)

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“…Decomposition cuts were developed in order to extend the concept of concavity cuts for deeper cuts [8,11,12]. Some other relevant research can also be found; see for example [2,4,5,14].…”

Section: Introductionmentioning

confidence: 99%

A dual method for polar cuts in disjoint bilinear programming

Ding,

Ma,

Chen

et al. 2024

Croat. oper. res. rev. (Online)

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As one branch of deterministic approaches to disjoint bilinear programming, cutting plane methods are renowned for its ability to systematically reduce the search space by adding cutting planes that are able to cut off regions deemed infeasible or suboptimal. Polar cuts have been widely utilized as a dominating type of cut in terms of deepness. During the establishment of a polar cut, the modified Newton's method is employed to derive the cutting points along the positive or negative extensions of edges emanating from a local solution. Nonetheless, its performance can be further improved along the positive extensions. Drawing inspiration from integer programming, we develop a new approach based on the LP duality theory for this purpose. It re-formulates the original program with a piece-wise linear concave objective function as a single LP. Moreover, we propose a new technique to derive the edges as accommodation to degeneracy. Numerical results show that, by utilizing our newly developed dual method, computing time can be gradually saved as the percentage of generated cutting points along the positive extensions of edges rises.

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“…Decomposition cuts were developed in order to extend the concept of concavity cuts for deeper cuts [8,11,12]. Some other relevant research can also be found; see for example [2,4,5,14].…”

Section: Introductionmentioning

confidence: 99%

A dual method for polar cuts in disjoint bilinear programming

Ding,

Ma,

Chen

et al. 2024

Croat. oper. res. rev. (Online)

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“…Later, Kheirfam [18] extended the method to 𝑃 * (𝑘)-horizontal linear complementarity problems, while Guerra [16] applied it to the SDO case. For more related papers about Darvay and Takàcs' technique, we refer to (see e.g., [11,19,20]).…”

mentioning

confidence: 99%

Interior-point algorithm for linear programming based on a new descent direction

Billel,

Djamel,

Aicha

et al. 2023

RAIRO-Oper. Res.

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We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t) = t7\4. Furthermore, we show that the algorithm finds the ϵ-optimal solution of the underlying problem in polynomial time, namely O(√nlog(n+3\7√2)) iterations. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.

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