A primal–dual interior point method for a novel type-2 second order cone optimization

Md Sarowar Morshed; Chrysafis Vogiatzis; Md Noor-E-Alam

doi:10.1016/j.rico.2021.100042

A primal–dual interior point method for a novel type-2 second order cone optimization

Md Sarowar Morshed, Chrysafis Vogiatzis, Md Noor-E-Alam

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO problem. We then develop a primal–dual interior point algorithm for solving a type-2 second order conic optimization problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive a new iteration bound for our framework.

Original language	English (US)
Article number	100042
Journal	Results in Control and Optimization
Volume	4
DOIs	https://doi.org/10.1016/j.rico.2021.100042
State	Published - Sep 2021
Externally published	Yes

Keywords

Interior point methods
Kernel functions
Primal–dual methods
Second order cone optimization

ASJC Scopus subject areas

Control and Optimization
Artificial Intelligence
Applied Mathematics
Control and Systems Engineering
Modeling and Simulation

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10.1016/j.rico.2021.100042

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abstract = "In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO problem. We then develop a primal–dual interior point algorithm for solving a type-2 second order conic optimization problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive a new iteration bound for our framework.",

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AU - Morshed, Md Sarowar

AU - Vogiatzis, Chrysafis

AU - Noor-E-Alam, Md

PY - 2021/9

Y1 - 2021/9

N2 - In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO problem. We then develop a primal–dual interior point algorithm for solving a type-2 second order conic optimization problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive a new iteration bound for our framework.

AB - In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO problem. We then develop a primal–dual interior point algorithm for solving a type-2 second order conic optimization problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive a new iteration bound for our framework.

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KW - Kernel functions

KW - Primal–dual methods

KW - Second order cone optimization

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A primal–dual interior point method for a novel type-2 second order cone optimization

Abstract

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