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An adaptively regularized sequential quadratic programming method for equality constrained optimization

  • * Corresponding author: Songqiang Qiu

    * Corresponding author: Songqiang Qiu 

The first author is supported by the Fundamental Research Funds for the Central Universities 2014QNA62

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  • In this paper, we devise an adaptively regularized SQP method for equality constrained optimization problem that is resilient to constraint degeneracy, with a relatively small departure from classical SQP method. The main feature of our method is an adaptively choice of regularization parameter, embedded in a trust-funnel-like algorithmic scheme. Unlike general regularized methods, which update regularization parameter after a regularized problem is approximately solved, our method updates the regularization parameter at each iteration according to the infeasibility measure and the promised improvements achieved by the trial step. The sequence of regularization parameters is not necessarily monotonically decreasing. The whole algorithm is globalized by a trust-funnel-like strategy, in which neither a penalty function nor a filter is needed. We present global and fast local convergence under weak assumptions. Preliminary numerical results on a collection of degenerate problems are reported, which are encouraging.

    Mathematics Subject Classification: Primary: 65K05, 90C30, 90C55.


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  • Figure 1.  Performance compared to MINOS

    Figure 2.  Performance compared to LOQO

    Table 1.  Compared to MINOS

    Use MINOS'Stopping rule.
    MINOS New Alg.
    Problem solved
    $ <1500 $ evals.
    100 103
    ($ <1500 $ evals.)
    95.24% 98.10%
    Average evals
    ($ <1500 $ evals.)
    84.04 67.5
    Median evals
    ($ <1500 $ evals.)
    27 21
     | Show Table
    DownLoad: CSV

    Table 2.  Compared to LOQO.

    Use LOQO's Stopping rule.
    LOQONew Alg.
    Problem solved
    ($ <1500 $ evals.
    ($ <1500 $ evals.)
    Average evals
    ($ <1500 $ evals.)
    Median evals
    ($ <1500 $ evals.)
     | Show Table
    DownLoad: CSV
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