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A Two-Phase Gradient Method for Quadratic Programming Problems with a Single Linear Constraint and Bounds on the Variables

Daniela di Serafino, Gerardo Toraldo, Marco Viola, Jesse Barlow
2018 SIAM Journal on Optimization  
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables.  ...  This is based on a comparison between a measure of optimality in the reduced space and a measure of bindingness of the variables that are on the bounds, defined by extending the concept of proportioning  ...  We are concerned with the solution of Quadratic Programming problems with a Single Linear constraint and lower and upper Bounds on the variables (SLBQPs): min f (x) := 1 2 x T H x − c T x, s.t. q T x =  ... 
doi:10.1137/17m1128538 fatcat:7cxbexxmzvatxpalri6kyfixve

A two-variable linear program solves the standard linear–quadratic formulation of the fractionation problem in cancer radiotherapy

Fatemeh Saberian, Archis Ghate, Minsun Kim
2015 Operations Research Letters  
We prove that this formulation of the fractionation problem can in fact be solved to optimality by instead solving a two-variable linear program with a few constraints.  ...  The standard formulation of the fractionation problem with multiple organs-at-risk based on the linear-quadratic dose-response model requires the solution of a nonconvex quadratically constrained quadratic  ...  Results We show in Theorem 1 below the perhaps surprising result that an optimal solution to (OPTFRAC) can in fact be derived in closed-form from the solution of a two-variable linear program (LP) with  ... 
doi:10.1016/j.orl.2015.02.005 fatcat:cwj2es42xffkpdm7igygs47yye

Interactive fuzzy random two-level linear programming through fractile criterion optimization

Masatoshi Sakawa, Hideki Katagiri, Takeshi Matsui
2011 Mathematical and computer modelling  
To deal with the formulated two-level linear programming problems involving fuzzy random variables, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level linear programming  ...  Through the use of the fractile criterion optimization model, the transformed stochastic two-level programming problem can be reduced to a deterministic one.  ...  Fuzzy mathematical programming Fuzzy random variable Level set Two-level linear programming problem Fractile criterion optimization Interactive decision making Gaussian distribution a b s t r a c t In  ... 
doi:10.1016/j.mcm.2011.08.006 fatcat:okwndldd5fhfnllaww2paxqxlu

Solving a Fully Rough Integer Linear Fractional Programming Problem

El-Saeed Ammar, Tarek El jerbi
2019 Delta Journal of Science  
In this paper, a fully rough integer linear fractional programming problem is introduced, in which all coefficients and decision variables in the objective function and the constraints are rough intervals  ...  The optimal value of decision rough variables is rough interval. In order to solve this problem, we will construct four crisp integer linear fractional programming problems.  ...  The problems, where the objective function is a ratio of two linear functions subject to a set of linear constraints and nonnegative integer variables constitute an integer linear fractional programming  ... 
doi:10.21608/djs.2019.139195 fatcat:5yor2d6d7zgctd3xd64fssvba4

Formulation of linear problems and solution by a universal machine

B. Curtis Eaves, Uriel G. Rothblum
1994 Mathematical programming  
This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity  ...  echelon forms of matrices, and all quadratic programming problems with bounded variables.  ...  This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity  ... 
doi:10.1007/bf01581699 fatcat:zzxamwje2rdh7dda4kitik3jem

A novel approach for solving decision-making problems with stochastic linear-fractional models

Watheq Laith, Rasheed Al-Salih, Ali Habeeb
2021 Eastern-European Journal of Enterprise Technologies  
In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution.  ...  In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second  ...  On the other hand, in some real-world applications, the decision-maker has to formulate the problem as a ratio between two linear objective functions, and then the problem is known as a fractional linear  ... 
doi:10.15587/1729-4061.2021.241916 fatcat:53melforkva3lixr2yunmv2jiu

An Exponential Approximation Algorithm in Linear Programming

Victor Gordunovsky
2014 Procedia Computer Science  
The algorithm determines a non-iteration procedure for computing the optimal solution of a linear programming problem.  ...  We consider approximating system of linear equations to determine the optimal basis variables of the linear programming problem. The usefulness of the algorithm is illustrated by a numerical example.  ...  These inequalities transformed to a system of two equations with two variables 1 the problem (8) correspond to the two equations of the problem (9).  ... 
doi:10.1016/j.procs.2014.05.313 fatcat:u6tyk4strbfx3htzas2pqtapy4

Partitioning procedures for solving mixed-variables programming problems

J. F. Benders
2005 Computational Management Science  
Each step involves the solution of a general programming problem. The two procedures differ only in the way the linear programming problem is solved.  ...  The basic idea behind the procedures to be described in this report is a partitioning of the given problem (t.t) into two sub problems; a programming problem (which may be linear, non-linear, discrete,  ... 
doi:10.1007/s10287-004-0020-y fatcat:jd7e5rgzojgspdfnaomrnpoaea

Interactive Fuzzy Programming for Random Fuzzy Two-Level Integer Programming Problems through Fractile Criteria with Possibility

Masatoshi Sakawa, Takeshi Matsui
2013 Applied Mathematics  
This paper considers two-level integer programming problems involving random fuzzy variables with cooperative behavior of the decision makers.  ...  levels, the original random fuzzy two-level integer programming problems are reduced to deterministic ones.  ...  Further extensions to two-level linear programming problems with random variables, called stochastic two-level linear programming problems [15, 16] , two-level integer programming problems [17] , and  ... 
doi:10.4236/am.2013.48a006 fatcat:3g7eegekczat7obu2ecle6djiu

Linear Programming Problems: Determination of Optimal Value of Real Life Practical Problems

Dilaram Bhattarai
2018 NUTA Journal  
From the general point of view, the problems of control and planning are usually reduced to a choice of a certain system of numerical parameters or a function ensuring the most effective achievement of  ...  For the large number of practically interesting problems the objective function is expressed linearly in term of plan characteristics, the permissible values of the parameters also obeying linear equalities  ...  Graphical Methods of Solving a Linear Programming Problem If the objective function is a function of two variables, we can solve linear programming problems by the graphical method.  ... 
doi:10.3126/nutaj.v5i1-2.23461 fatcat:xpdkkrgecjefjkr6vzzf3odaia

PROPOSED PIECEWISE LINEAR APPROXIMATION FOR TACKLING NONLINEAR PROGRAMMING PROBLEMS WITH SEPARABLE OBJECTIVE FUNCTION

OGBONNA CHUKWUDI J ., OPARA JUDE ., IHEAGWARA ANDREW I ., IHEKUNA STEPHEN O .
2019 International Journal of Engineering Applied Sciences and Technology  
In the study, a program code via Wolfram Mathematica for evaluating a nonlinear separable quadratic objective function with multiple linear variables and constraints of different sizes up to 70,000 variables  ...  The two problems solved in this study showed that the proposed algorithm converged faster than solving the original problem directly via Wolfram Mathematica, though with the same optimal solution.  ...  Mathematical programming problem seeks to minimize (or maximize) a function of many variables subject to a set of constraints on these variables.  ... 
doi:10.33564/ijeast.2019.v04i03.055 fatcat:hwudrusnnzb65fjawh2uh7ckg4

A Dual Simplex Algorithm for Piecewise-Linear Programming

Faruk Güder, Francis J. Nourie
1996 Journal of the Operational Research Society  
A standard LP problem with nonnegativity constraints can be converted to a P-LP problem where each variable has only two breakpoints, zero and infinity.  ...  Vk Vr Vk Ve The traditional linear programming problem is a special case of P-LP.  ... 
doi:10.1057/jors.1996.63 fatcat:qbfue63aezb45ijakobvlodfuu

Page 5001 of Mathematical Reviews Vol. , Issue 88i [page]

1988 Mathematical Reviews  
G. (3-STMR) On solving two variables continuous parameter linear and quadratic programming problems. Utilitas Math. 30 (1986), 181-189.  ...  In particular, we demonstrate that the optimal solution to any two- variable continuous parameter linear or quadratic programming problem can always be expressed in terms of a single continuous parametric  ... 

Page 619 of The Journal of the Operational Research Society Vol. 50, Issue 6 [page]

1999 The Journal of the Operational Research Society  
linear programming can be very effective for solving problems with real or integer variables and linear constraints.'’  ...  Linear programming is very efficient in problems like the travel salesman problem where there is a linear objective function and linear constraint functions.  ... 

A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables

Kadriye Simsek Alan
2020 Cybernetics and Information Technologies  
AbstractIn this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed.  ...  linear programming problem.  ...  In [3] a new method was given, called variable reduction method for a classes of pure integer linear programming problems in single stage.  ... 
doi:10.2478/cait-2020-0045 fatcat:urcnikbz5fewdih6c5mzgaaxli
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