TY - JOUR
T1 - Simplex-type algorithm for second-order cone programmes via semi-infinite programming reformulation
AU - Hayashi, Shunsuke
AU - Okuno, Takayuki
AU - Ito, Yoshihiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI [grant number 26330022].
PY - 2016/11/1
Y1 - 2016/11/1
N2 - To solve the (linear) second-order cone programmes (SOCPs), the primal–dual interior-point method has been studied extensively so far and said to be the most efficient method by many researchers. On the other hand, the simplex-type method for SOCP is much less spotlighted, while it still keeps an important position for linear programmes. In this paper, we apply the dual–simplex primal-exchange (DSPE) method, which was originally developed for solving linear semi-infinite programmes, to the SOCP by reformulating the second-order cone constraint as an infinite number of linear inequality constraints. Then, we show that the sequence generated by the DSPE method converges to the SOCP optimum under certain assumptions. In the numerical experiments, we consider the situation to solve multiple SOCPs with similar structures successively. Then we observe that our simplex-type method can be more efficient than the existing interior-point method when we apply the so-called ‘hot start’ technique.
AB - To solve the (linear) second-order cone programmes (SOCPs), the primal–dual interior-point method has been studied extensively so far and said to be the most efficient method by many researchers. On the other hand, the simplex-type method for SOCP is much less spotlighted, while it still keeps an important position for linear programmes. In this paper, we apply the dual–simplex primal-exchange (DSPE) method, which was originally developed for solving linear semi-infinite programmes, to the SOCP by reformulating the second-order cone constraint as an infinite number of linear inequality constraints. Then, we show that the sequence generated by the DSPE method converges to the SOCP optimum under certain assumptions. In the numerical experiments, we consider the situation to solve multiple SOCPs with similar structures successively. Then we observe that our simplex-type method can be more efficient than the existing interior-point method when we apply the so-called ‘hot start’ technique.
KW - linear semi-infinite programme
KW - second-order cone programme
KW - simplex method
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U2 - 10.1080/10556788.2015.1121487
DO - 10.1080/10556788.2015.1121487
M3 - Article
AN - SCOPUS:84951266234
VL - 31
SP - 1272
EP - 1297
JO - Optimization Methods and Software
JF - Optimization Methods and Software
SN - 1055-6788
IS - 6
ER -