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Reducing the high computational cost of large convolutional neural networks is crucial when deploying the networks to resource-constrained environments. We first show the greedy approach of recent channel pruning methods ignores the inherent quadratic coupling between channels in the neighboring layers and cannot safely remove inactive weights during the pruning procedure. Furthermore, due to these inactive weights, the greedy methods cannot guarantee to satisfy the given resource constraints and deviate with the true objective. In this regard, we propose a novel channel selection method that optimally selects channels via discrete QCQP, which provably prevents any inactive weights and guarantees to meet the resource constraints tightly in terms of FLOPs, memory usage, and network size. We also propose a quadratic model that accurately estimates the actual inference time of the pruned network, which allows us to adopt inference time as a resource constraint option. Furthermore, we generalize our method to extend the selection granularity beyond channels and handle non-sequential connections. Our experiments on CIFAR-10 and ImageNet show our proposed pruning method outperforms other fixed-importance channel pruning methods on various network architectures.