AN IMPROVED REDUCTION METHOD FOR THE ROBUST OPTIMIZATION OF THE ASSIGNMENT PROBLEM

2012 ◽  
Vol 29 (05) ◽  
pp. 1250032 ◽  
Author(s):  
BYUNGJUN YOU ◽  
DAISUKE YOKOYA ◽  
TAKEO YAMADA
Keyword(s):  
Lower Bound ◽  
Exact Solutions ◽  
Upper Bound ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
Reduction Method ◽  
Computation Time ◽  
Approximate Solutions ◽  
Cpu Time ◽  
Surrogate Relaxation

We are concerned with a variation of the assignment problem, where the assignment costs differ under different scenarios. We give a surrogate relaxation approach to derive a lower bound and an upper bound quickly, and show that the pegging test known for zero–one programming problems is also applicable to this problem. Next, we discuss how the computation time for pegging can be shortened by taking the special structure of the assignment problem into account. Finally, through numerical experiments we show that the developed method finds exact solutions for instances with small number of scenarios in relatively small CPU time, and good approximate solutions in case of many scenarios.

scholarly journals Modified variational iteration method for variant Boussinesq equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1195-1199 ◽  
Author(s):  
Jun-Feng Lu
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Boussinesq Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

In this paper, we solve the variant Boussinesq equation by the modified variational iteration method. The approximate solutions to the initial value problems of the variant Boussinesq equation are provided, and compared with the exact solutions. Numerical experiments show that the modified variational iteration method is efficient for solving the variant Boussinesq equation.

scholarly journals Improved Bounds for Radiok-Chromatic Number of HypercubeQn

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Laxman Saha ◽  
Pratima Panigrahi ◽  
Pawan Kumar
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Graph Coloring ◽  
Upper Bound ◽  
Channel Assignment ◽  
Assignment Problem ◽  
Communication Problem ◽  
Channel Assignment Problem

A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels (nonnegative integers) to the stations in an optimal way such that interference is avoided as reported by Hale (2005). Radiok-coloring of a graph is a special type of channel assignment problem. Kchikech et al. (2005) have given a lower and an upper bound for radiok-chromatic number of hypercubeQn, and an improvement of their lower bound was obtained by Kola and Panigrahi (2010). In this paper, we further improve Kola et al.'s lower bound as well as Kchikeck et al.'s upper bound. Also, our bounds agree for nearly antipodal number ofQnwhenn≡2(mod 4).

ON RADIO NUMBER OF POWER OF CYCLES

2011 ◽  
Vol 04 (03) ◽  
pp. 523-544 ◽  
Author(s):  
Laxman Saha ◽  
Pratima Panigrahi ◽  
Pawan Kumar
Keyword(s):  
Lower Bound ◽  
Graph Coloring ◽  
Upper Bound ◽  
Channel Assignment ◽  
Assignment Problem ◽  
Arbitrary Graph ◽  
Communication Problem ◽  
Channel Assignment Problem ◽  
Radio Number

A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels (non-negative integers) to the stations in an optimal way such that interference is avoided, see Hale [4]. The radio coloring of a graph is a special type of channel assignment problem. Here we develop a technique to find an upper bound for radio number of an arbitrary graph and also we give a lower bound for the same. Applying these bounds we have obtained radio number of [Formula: see text], r ⩾ 3, for several values of n and r. Moreover for diameter 2 or 3 radio number of [Formula: see text] have been determined completely for all values of n and r.

scholarly journals Nearly Optimal Regret for Stochastic Linear Bandits with Heavy-Tailed Payoffs

2020 ◽  
Author(s):  
Bo Xue ◽  
Guanghui Wang ◽  
Yimu Wang ◽  
Lijun Zhang
Keyword(s):  
Lower Bound ◽  
Financial Markets ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Time Horizon ◽  
Contextual Information ◽  
Finite Action ◽  
Heavy Tailed ◽  
Novel Algorithms ◽  
Regret Bound

In this paper, we study the problem of stochastic linear bandits with finite action sets. Most of existing work assume the payoffs are bounded or sub-Gaussian, which may be violated in some scenarios such as financial markets. To settle this issue, we analyze the linear bandits with heavy-tailed payoffs, where the payoffs admit finite 1+epsilon moments for some epsilon in (0,1]. Through median of means and dynamic truncation, we propose two novel algorithms which enjoy a sublinear regret bound of widetilde{O}(d^(1/2)T^(1/(1+epsilon))), where d is the dimension of contextual information and T is the time horizon. Meanwhile, we provide an Omega(d^(epsilon/(1+epsilon))T^(1/(1+epsilon))) lower bound, which implies our upper bound matches the lower bound up to polylogarithmic factors in the order of d and T when epsilon=1. Finally, we conduct numerical experiments to demonstrate the effectiveness of our algorithms and the empirical results strongly support our theoretical guarantees.

MONTE CARLO EVALUATION OF AMERICAN OPTIONS USING CONSUMPTION PROCESSES

2006 ◽  
Vol 09 (04) ◽  
pp. 455-481 ◽  
Author(s):  
DENIS BELOMESTNY ◽  
GRIGORI N. MILSTEIN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lower Bound ◽  
Upper Bound ◽  
Continuous Time ◽  
Numerical Experiments ◽  
American Options ◽  
Upper And Lower Bounds ◽  
New Approach ◽  
Monte Carlo Evaluation

We develop a new approach for pricing both continuous-time and discrete-time American options which is based on the fact that any American option is equivalent to a European one with a consumption process involved. This approach admits the construction of an upper bound (a lower bound) on the true price using some lower bound (an upper bound) by Monte Carlo simulation. A number of effective estimators of upper and lower bounds with the reduced variance are proposed. The method is supported by numerical experiments which look promising.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Isolated minima of the product of n linear forms

1953 ◽  
Vol 49 (1) ◽  
pp. 59-62 ◽  
Author(s):  
E. S. Barnes
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Linear Forms ◽  
Image Position

Letbe n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

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