A smoothing Newton method for second-order cone optimization based on a new smoothing function

Tang, Jingyong; He, Guoping; Dong, Li; Fang, Liang

doi:10.1016/j.amc.2011.06.015

Cited by 20 publications

(17 citation statements)

References 28 publications

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“…With an SOC complementarity function, one (e.g., [2], [3], [5], [6], [18], [19]) can rewrite (1.1) as:…”

Section: The Algorithmmentioning

confidence: 99%

“…Step 5: A similar algorithmic framework has been extensively studied for solving the SOCP (see, e.g., [2], [3], [5], [6], [18], [19]). However, all papers mentioned above discussed this kind of algorithms based on a monotone line search.…”

Section: A L G O R I T H M 31 (A Non-monotone Smoothing-type Algoritmentioning

confidence: 99%

“…The proposed algorithm is based on a non-monotone line search scheme, which was first introduced by Zhang and Hager [20], and includes the usual monotone line search (e.g., see [2], [3], [5], [6], [18], [19]). By using the theory of Euclidean Jordan algebras, we prove the global and local quadratical convergence of the proposed algorithm under suitable assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, the SOCP has been studied extensively due to its various applications in many fields (see [1], [15]). Various methods have been developed for solving the SOCP, where the smoothing-type algorithms (e.g., [2], [3], [5], [6], [18], [19]) are one of the most effective methods. This kind of algorithms reformulates the system (1.1) as a family of parameterized smooth equations and solve the smooth equations approximately by using Newton's method at each iteration.…”

Section: Introductionmentioning

confidence: 99%

“…By driving the parameter to converge to zero, one can expect to find a solution to the SOCP. In general, the smoothing-type algorithms for the SOCP are designed based on a monotone line search (e.g., [2], [3], [5], [6], [18], [19]). It is well known that the non-monotone line search rule has many advantages, especially in the case of iterates trapped in a narrow curved valley of objective functions (e.g., [8], [20]).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

et al. 2015

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“…With an SOC complementarity function, one (e.g., [2], [3], [5], [6], [18], [19]) can rewrite (1.1) as:…”

Section: The Algorithmmentioning

confidence: 99%

Section: A L G O R I T H M 31 (A Non-monotone Smoothing-type Algoritmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

et al. 2015

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Improved Gauss Seidel based projection–contraction algorithm for the mixed complementarity problem in contact problem

Zeng

Zheng

Liu

et al. 2022

Num Anal Meth Geomechanics

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The GSCP (Gauss–Seidel based projection‐contraction) algorithm has been well established in solving elastoplastic mixed complementarity problems (MiCPs) or other problems which have similar mathematical form. However, the stability problems in the GSPC algorithm may cause nonconvergence or program crashes. Thus, the method of constructing and analyzing counterexamples is adopted to study the reasons for the instability of the GSPC algorithm. The R‐GSPC algorithm was developed by modifying the part of the GSPC algorithm that caused the crash to make the algorithm stable. In addition, this paper analyzes the convergence, compatibility, and initial value impact of R‐GSPC, and finds that the R‐GSPC algorithm greatly improves the robustness and stability without losing accuracy. This paper allows the GSPC algorithm to be better extended to more fields and to be suitabled for being introduced into commercial programs.

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A smoothing Newton method for the second-order cone complementarity problem

Tang

Dong

et al. 2013

Appl Math

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A smoothing Newton method for the second-order cone complementarity problem Applications of Mathematics, Vol. 58 (2013) Abstract. In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.

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A smoothing Newton method for second-order cone optimization based on a new smoothing function

Cited by 20 publications

References 28 publications

Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

Improved Gauss Seidel based projection–contraction algorithm for the mixed complementarity problem in contact problem

A smoothing Newton method for the second-order cone complementarity problem

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