An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters is presented. This problem, which arises in microwave power transmission from solar power satellites, is to maximize the array gain in a desired direction with the gain loss of the phase shifters taken into account. In this paper the problem is first formulated as a discrete optimization problem, which is then decomposed into element-wise subproblems by the real rotation theorem. Based on this approach, a polynomial-time algorithm to solve the problem numerically is constructed and its effectiveness is verified by numerical simulations.

This paper proposes a suboptimal algorithm for the maximum likelihood detection (MLD) in multiple-input multiple-output (MIMO) communications. The proposed algorithm regards transmitted signals as continuous variables in the same way as a common method for the discrete optimization problem, and then searches for candidates of the transmitted signals in the direction of a modified gradient vector of the metric. The vector is almost proportional to the direction of the noise enhancement, from which zero-forcing (ZF) or minimum mean square error (MMSE) algorithms suffer. This method sets the initial guess to the solution by ZF or MMSE algorithms, which can be recursively calculated. Also, the proposed algorithm has the same complexity order as that of conventional suboptimal algorithms. Computer simulations demonstrate that it is much superior in BER performance to the conventional ones.

L-convex functions are nonlinear discrete functions on integer points that are computationally tractable in optimization. In this paper, a discrete Hessian matrix and a local quadratic expansion are defined for L-convex functions. We characterize L-convex functions in terms of the discrete Hessian matrix and the local quadratic expansion.

M-convex functions have various desirable properties as convexity in discrete optimization. We can find a global minimum of an M-convex function by a greedy algorithm, i.e., so-called descent algorithms work for the minimization. In this paper, we apply a scaling technique to a greedy algorithm and propose an efficient algorithm for the minimization of an M-convex function. Computational results are also reported.

This paper develops an algorithm based on the Modular Approach to solve singly constrained separable discrete optimization problems (Nonlinear Knapsack Problems). The Modular Approach uses fathoming and integration techniques repeatedly. The fathoming reduces the decision space of variables. The integration reduces the number of variables in the problem by combining several variables into one variable. Computational experiments for "hard" test problems with up to 1000 variables are provided. Each variable has up to 1000 integer values.