A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming

2013 ◽  
Vol 23 (4) ◽  
pp. 2320-2340 ◽  
Author(s):  
Naohiko Arima ◽  
Sunyoung Kim ◽  
Masakazu Kojima
Keyword(s):  
Optimization Model ◽  
Quadratic Optimization ◽  
Positive Cone ◽  
Completely Positive ◽  
Cone Programming ◽  
Completely Positive Cone ◽  
Constrained Quadratic Optimization ◽  
Quadratically Constrained

scholarly journals The cone of Z-transformations on Lorentz cone

2019 ◽  
Vol 35 ◽  
pp. 387-393 ◽  
Author(s):  
Sandor Nemeth ◽  
Muddappa Gowda
Keyword(s):  
Structural Properties ◽  
Positive Cone ◽  
Linear Program ◽  
Completely Positive ◽  
Completely Positive Cone ◽  
Lorentz Cone ◽  
Semidefinite Cone

In this paper, the structural properties of the cone of $\calz$-transformations on the Lorentz cone are described in terms of the semidefinite cone and copositive/completely positive cones induced by the Lorentz cone and its boundary. In particular, its dual is described as a slice of the semidefinite cone as well as a slice of the completely positive cone of the Lorentz cone. This provides an example of an instance where a conic linear program on a completely positive cone is reduced to a problem on the semidefinite cone.

scholarly journals The automorphism group of a completely positive cone and its Lie algebra

2013 ◽  
Vol 438 (10) ◽  
pp. 3862-3871 ◽  
Author(s):  
M. Seetharama Gowda ◽  
Roman Sznajder ◽  
Jiyuan Tao
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Positive Cone ◽  
Completely Positive ◽  
Completely Positive Cone

scholarly journals A New Conic Approach to Semisupervised Support Vector Machines

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ye Tian ◽  
Jian Luo ◽  
Xin Yan
Keyword(s):  
Quadratic Forms ◽  
Optimal Solution ◽  
Positive Cone ◽  
Support Vector ◽  
Completely Positive ◽  
Adaptive Scheme ◽  
Completely Positive Cone ◽  
Vector Machines ◽  
Programming Techniques ◽  
Completely Positive Programming

We propose a completely positive programming reformulation of the 2-norm soft marginS3VMmodel. Then, we construct a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones to approximate the underlying completely positive cone. Anϵ-optimal solution can be found in finite iterations using semidefinite programming techniques by our method. Moreover, in order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature.

scholarly journals Characterization of Robust Solution Quadratically Constrained Quadratic Optimization Problem Subjected to Data Uncertainty

2021 ◽  
pp. 1-23
Author(s):  
Moussa BARRO ◽  
Satafa SANOGO ◽  
Mohamed ZONGO ◽  
Sado TRAORÉ
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Real Life ◽  
Quadratic Optimization ◽  
Data Uncertainty ◽  
Robust Solution ◽  
Quadratic Optimization Problem ◽  
Robust Duality ◽  
Constrained Quadratic Optimization ◽  
Quadratically Constrained

Robust Optimization (RO) arises in two stages of optimization, first level for maximizing over the uncertain data and second level for minimizing over the feasible set. It is the most suitable mathematical optimization procedure to solve real-life problem models. In the present work, we characterize robust solutions for both homogeneous and non-homogeneous quadratically constrained quadratic optimization problem where constraint function and cost function are uncertain. Moreover, we discuss about optimistic dual and strong robust duality of the considered uncertain quadratic optimization problem. Finally, we complete this work with an example to illustrate our solution method. Mathematics Subject Classification: (2010) 90C20 - 90C26 - 90C46-90C47 Keywords: Robust Optimization, Data Uncertainty, Quadratic Optimization Strong Duality, Robust Solution, DPJ-Convex.

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