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With technology scaling, the trend for high-performance integrated circuits is toward ever higher operating frequency, lower power supply voltages, and higher power dissipation. This causes a dramatic increase in the currents being delivered through the on-chip power grid and is recognized in the 2001 International Technology Roadmap for Semiconductors as one of the difficult challenges. The addition of decoupling capacitances (decaps) is arguably the most powerful degree of freedom that a designer has for power-grid noise abatement and is becoming more important as technology scales. In this paper, we propose and demonstrate an algorithm for the automated placement and sizing of decaps in application specific integrated circuit (ASIC)-like circuits. The problem is formulated as one of nonlinear optimization and is solved using a sensitivity-based quadratic programming (QP) solver. The adjoint sensitivity method is applied to calculate the first-order sensitivities. We propose a fast convolution technique based on piecewise linear (PWL) compressions of the original and adjoint waveforms. Experimental results show that power grid noise can be significantly reduced after a judicious optimization of decap placement, with little change in the total chip area.