Topic
Supporting hyperplane
About: Supporting hyperplane is a research topic. Over the lifetime, 121 publications have been published within this topic receiving 1197 citations.
Papers published on a yearly basis
Papers
1 Jan 1978
TL;DR: In this paper, the problem of finding optimal reservoir capacities by minimizing total building cost eventually plus a penalty, where a reliability type constraint is prescribed, further lower and upper bounds for the capacities are prescribed.
Abstract: Mathematically a natural river system is a rooted directed tree where the orientations of the edges coincide with the directions of the streamflows. Assume that in some of the river valleys it is possibie to build reservoirs the purpose of which will be to retain the flood, once a year, say. The problem is to find optimal reservoir capacities by minimizing total building cost eventually plus a penalty, where a reliability type constraint, further lower and upper bounds for the capacities are prescribed. The solution of the obtained nonlinear programming problem is based on the supporting hyperplane method of Veinott combined with simulation of multivariate probability distributions. Numerical illustrations are given.
91 citations
TL;DR: This research theoretically explores the measurement of RTS under a possible occurrence of multiple solutions in DEA (Data Envelopment Analysis) and makes it possible to measure a degree of scale economies (RTS) under the simultaneous occurrence of Type I and Type II.
62 citations
TL;DR: The rate region of Gaussian multiple description coding with individual and central distortion constraints is completely characterized and a lower bound and an upper bound are derived for each supporting hyperplane of the rate region.
Abstract: The rate region of Gaussian multiple description coding with individual and central distortion constraints is completely characterized. Specifically, a lower bound and an upper bound are derived for each supporting hyperplane of the rate region, where the lower bound is associated with a max-min game while the upper bound is associated with a min-max game; furthermore, it is shown that these two bounds coincide due to the existence of a saddle point.
56 citations
TL;DR: In this paper, a new formulation of the most general case of multiphase, multireaction (chemical) equilibrium, and two new global chemical equilibrium criteria arising from it are presented.
Abstract: We present a new formulation of the most general case of multiphase, multireaction (chemical) equilibrium, and two new global chemical equilibrium criteria arising from it. This formulation involves the new concept of a phase class, which allows the most general case in which every substance need not occur in every phase of the system (as in the important case where pure condensed phases are present in addition to multispecies phases). This is coupled with a particular choice of variables for each phase class in the problem formulation. The two new criteria resulting from this formulation are: (1) a necessary and sufficient condition that must be satisfied by all feasible phase compositions and amounts at the global minimum of the Gibbs function, (2) a supporting hyperplane criterion for each phase class, which is also a necessary and sufficient condition that must be satisfied by all phase compositions for each phase class at such a global minimum
53 citations
TL;DR: In this article, a generalization of geometric programming called the signomial programming (MM) algorithm is proposed, which can converge to a boundary point or to one point of a continuum of minimum points.
Abstract: This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
48 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 7 |
| 2020 | 7 |
| 2019 | 6 |
| 2018 | 5 |
| 2017 | 3 |
| 2016 | 5 |