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This book presents novel approaches for efficient optimization techniques based on numerical simulations for photonic devices. It presents the recent advances in the application of the adjoint variable method to photonic devices as an efficient technique for sensitivity analysis. It also presents novel approaches for formulating the design of any photonic devices as an optimization problem. These optimization problems are then solved efficiently using gradient-based optimization algorithms. This book is the first one that shows how the optimization problem can be formulated as a convex optimization problem in photonics. Convex optimization programming allows for efficient solution of the design problem using interior point method. These approaches will highly accelerate the design cycle of novel structures to meet the ever demanding requirements of the photonic devices.