Input: The upper triangular matrix with positive diagonal entries, the vector | , the lower bound vector , the upper bound vector | u = , the initial hyper-ellipsoid bound . | Output: The solution to the BILS Problem (18). | Step 1. (Initialization) Set , , | Compute , , | , , | , . | Step 2. Compute , | if and , then | Go to Step 3 | else | Go to Step 4 | end if | Step 3. Set , | Compute , | , , , | , . | Go to Step 2 | Step 4. If , then | Set , , , | else if , then | Terminate | else | | if , then | | repeat | if , then | Terminate | end if | | until | if , then | | end if | end if | end if | Step 5. If , then | Set | Compute | else if , then | Set | Compute | else | Compute , | end if | Compute | Go to Step 2. |
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