Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.

A finite algorithm for concave minimization over a polyhedron

Abstract: We present a new algorithm for solving the problem of minimizing a nonseparable concave function over a polyhedron. The algorithm is of the branch-and-bound type. It finds a globally optimal extreme point solution for this problem in a finite number of steps. One of the major advantages of the algorithm is that the linear programming subproblems solved during the branch-and-bound search each have the same feasible region. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some preliminary computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several bilinear programming problems with the code.

On some new inequalities for differentiable co-ordinated convex functions

Abstract: Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in two variables are obtained. Mathematics Subject Classification (2000): 26A51; 26D15

Energy-Efficient Optimization for Downlink Massive MIMO FDD Systems With Transmit-Side Channel Correlation

Abstract: The energy-efficient resource allocation problem is investigated for the downlink massive multiple-input–multiple-output (MIMO) frequency-division duplexing (FDD) system under a correlated Rayleigh fading channel. Our objective is to maximize energy efficiency by adjusting the training duration, training power, and data power, under the constraint of the total transmit energy and spectral efficiency requirement for the user, which evaluates the impacts of the training and data transmission phases simultaneously. The optimization problem is established in a complicated form, where the difficulties lie in the nonanalytic expression of the involved objective function, as well as the nonconvex nature of the optimization problem. To solve it, the deterministic equivalent approximation methodology is introduced to obtain an accurate analytical expression of the cost function. Based on this, the optimization problem in a nonconvex fractional form is transformed into an equivalent optimization problem with a parametric subtractive form, which is still nonconvex. Thus, the objective function is lower bounded by a concave function, which leads to the availability of standard convex theory, and finally, an iterative resource allocation algorithm is proposed. Moreover, we obtain the closed-form solutions using the Lambert W function for some special channel cases. Numerical results validate the benefits of the proposed scheme and illustrate the tradeoff between training and data transmission.