A Polynomial Time Algorithm for the Resource Allocation Problem with a Convex Objective Function

An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

“…Using (2.9), (2.10) and (2.11), condition (2.5) can be written as follows Since the optimal solution x * to problem (CSL) depends on λ, we consider components of x * as functions of λ for different λ ∈ R 1 + : . In order that (3.1) and (2.6) ≡ (1.2) be satisfied, there exists some λ 6) which means that the inequality constraint (1.2) is satisfied with an equality for λ * in this case.…”

“…It turns out that some problems, arising in production planning and scheduling, in allocation of resources [2,6,7,14], in decision making [2,7,10,12,14], in the theory of search, in subgradient optimization, in facility location [10,12,13], and so forth, can be described mathematically by using problems like (CSL) and (CSLE), defined by (1.1)-(1.3) and (1.4)-(1.6), respectively. That is why, in order to solve such practical problems, we need some results and methods for solving (CSL) and (CSLE).…”

“…Related problems and methods for them are considered, for example, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

“…Algorithms for resource allocation problems are proposed in [2,6,7,14]. Algorithms for facility location problems are suggested in [10,12], and so forth.…”

On the solution of multidimensional convex separable continuous knapsack problem with bounded variables

“…Algorithms for bound constrained quadratic programming problems are proposed in Dembo and Tulowitzki (1983), Moré and Toraldo (1989), Pardalos and Kovoor (1990). A polynomial time algorithm for the resource allocation problem with a convex objective function and nonnegative integer variables is suggested in Katoh, Ibaraki, and Mine (1979). Surrogate upper bound sets for biobjective bi-dimensional binary knapsack problems are studied in Cerqueus, Przybylski, and Gandibleux (2015).…”