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Concave function
About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.
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3 citations
01 Jan 1989
TL;DR: In this paper, a decomposition method for finding saddle points of a function φ:X × Y → ℝ is characterized by an alternating succession of master programs and subprograms, which determine the proper iteration points, which are approximate saddle points over a subset Xn × Yn of the original domain.
Abstract: Decomposition methods for finding saddle points of a function φ:X × Y → ℝ are characterized by an alternating succession of master programs and subprograms [7]. The master programs determine the proper iteration points, which are approximate saddle points over a subset Xn × Yn of the original domain. The subprograms calculate auxiliary points, which serve to update the subset under consideration. For certain structured problems the subprograms may decompose; this fact accounts for the name and the practical importance of decomposition methods, but is not essential for their mathematical theory of convergence, which is our main concern here.
3 citations
TL;DR: In this article, the equivalence results between a convex and a concave transport cost are reexamined by assuming an arbitrary length, and the solution found shows that the relation depends on the space length.
Abstract: This article depicts a location game in a circular market. The equivalence results between a convex and a concave transport cost are reexamined by assuming an arbitrary length. In contrast to previous research the solution found shows that the equivalence relationship depends on the space length. Furthermore, the analysis is extended to a circular model with unitary length and zoning. In this case equivalence does not hold. Moreover, non-existence of equilibrium is shown under strictly linear quadratic functions. Surprisingly, equilibrium exists for a concave quadratic function but not for a convex quadratic function.
3 citations
TL;DR: It is shown that the algorithm shares a monotonicity property of Hassin’s algorithm, and the trajectory of the solutions generated by the algorithm is a “shortest” path from the initial solution to the “nearest” optimal solution.
Abstract: ow problem is known to be formulated as maximization of a polyhedral L-concave function. It is recently pointed out by Murota and Shioura (2014) that Hassin’s algorithm can be recognized as a steepest ascent algorithm for polyhedral L-concave functions. The objective of this paper is to show some monotonicity properties of the steepest ascent algorithm for polyhedral L-concave functions. We show that the algorithm shares a monotonicity property of Hassin’s algorithm. Moreover, the algorithm nds the
earest" optimal solution to a given initial solution, and the trajectory of the solutions generated by the algorithm is a \shortest" path from the initial solution to the
earest" optimal solution. The algorithm and its properties can be extended for polyhedral L ♮ -concave functions.
3 citations