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An integer programming approach for linear programs with probabilistic constraints

James Luedtke, Shabbir Ahmed, George L. Nemhauser
2008 Mathematical programming  
Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex.  ...  We give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint. We obtain two strengthened formulations.  ...  Acknowledgements The authors express thanks to the anonymous referees for comments that helped significantly improve the presentation of this paper.  ... 
doi:10.1007/s10107-008-0247-4 fatcat:y7vhg4jwdvabro5e6365eqi3bu

An Integer Programming Approach for Linear Programs with Probabilistic Constraints [chapter]

James Luedtke, Shabbir Ahmed, George Nemhauser
Integer Programming and Combinatorial Optimization  
Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex.  ...  We give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint. We obtain two strengthened formulations.  ...  Acknowledgements The authors express thanks to the anonymous referees for comments that helped significantly improve the presentation of this paper.  ... 
doi:10.1007/978-3-540-72792-7_31 dblp:conf/ipco/LuedtkeAN07 fatcat:ezinjluypfarbdulezydpydvtm

Optimization under uncertainty: state-of-the-art and opportunities

Nikolaos V. Sahinidis
2004 Computers and Chemical Engineering  
The paper begins with an overview of the main approaches to optimization under uncertainty: stochastic programming (recourse models, robust stochastic programming, and probabilistic models), fuzzy programming  ...  We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming  ...  Thanks are due to an anonymous referee for comments that helped increase the subjects covered in this paper.  ... 
doi:10.1016/j.compchemeng.2003.09.017 fatcat:fzemoqbejvcdvgi5f34mpvw3lq

Page 2773 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
From the text: “Conclusions: We have shown that an estimate of the number of operations for exact solution of an arbitrary linear integer programming problem with a fixed number of constraints 90C Mathematical  ...  A. (2-KIEVP) 87e:90070 Analysis of complexity estimates of exact algorithms for solving the general linear integer programming problem.  ... 

Applications of inexact programming methods to waste management under uncertainty: current status and future directions

Wei Sun, Chunjiang An, Gongchen Li, Ying Lv
2014 Environmental Systems Research  
, interval-parameter programming, mixed-integer programming, multiple-objective programming, and nonlinear programming.  ...  The demanding areas for future research efforts would include: expansion of conventional concepts to quantify uncertainties, integration of single inexact programming method with other programming methods  ...  Acknowledgement This research was supported by the Natural Sciences Foundation of China (71303017), the Program for Innovative Research Team (IRT1127), the MOE Key Project Program (311013), the Natural  ... 
doi:10.1186/s40068-014-0015-9 fatcat:3gpvi2pobrg4znwlag55wq52am

Page 1432 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
N. (4-LNDIC-CKE; London) An algorithm for the solution of multiparametric mixed integer linear programming problems.  ...  The author presents an algorithmic solution to mixed integer non- linear programs (MINLP) via integration of branch-and-bound techniques with an SQP solver.  ... 

Page 1209 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
The author considers a linear program with probabilistic con- straints and its dual.  ...  of a finite number of linear programming problems, formulated in a special way, with interval constraints.  ... 

On the solution of stochastic multiobjective integer linear programming problems with a parametric study

2009 Journal of the ACS Advances in Computer Science  
In this study we consider a multiobjective integer linear stochastic programming problem with individual chance constraints.  ...  We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. Some stability notions for such problem are characterized.  ...  PROBLEM STATEMENT AND THE SOLUTION CONCEPT The chance-constrained multiobjective integer linear programming problem with random parameters in the right-hand side of the constraints can be stated as follows  ... 
doi:10.21608/asc.2009.158225 fatcat:rkjwb5d5snbi7ph7nbmfvh6hma

Page 1398 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
programs with probabilistic constraints.  ...  Chapters 7 and 8 deal with computational approaches for multistage problems and for stochastic integer programs.  ... 

Static analysis for probabilistic programs

Sriram Sankaranarayanan, Aleksandar Chakarov, Sumit Gulwani
2013 Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13  
We propose an approach for the static analysis of probabilistic programs that sense, manipulate, and control based on uncertain data.  ...  Each path yields interval bounds that can be summed up with a "coverage" bound to yield an interval that encloses the probability of assertion for the program as a whole.  ...  Michael Hicks and the anonymous reviewers for their detailed comments.  ... 
doi:10.1145/2491956.2462179 dblp:conf/pldi/SankaranarayananCG13 fatcat:5l7vkdhtgjhspn7r5ouitebhv4

Page 507 of Mathematical Reviews Vol. , Issue 93a [page]

1993 Mathematical Reviews  
In Section 1 the linearization approach for quadratic mixed-integer problems is developed.  ...  507 90C Mathematical programming 93a:90042 90C08 49K45 90C15 Todd, Michael J. (1-CRNL-OR) Probabilistic models for linear programming. Math. Oper. Res. 16 (1991), no. 4, 671-693.  ... 

Counting the Number of Solutions to Constraints [article]

Jian Zhang, Cunjing Ge, Feifei Ma
2020 arXiv   pre-print
The constraints may take various forms, including, formulas in the propositional logic, linear inequalities over the reals or integers, Boolean combination of linear constraints.  ...  Compared with constraint satisfaction problems, counting problems have received less attention.  ...  Solution Counting for Linear Constraints A linear constraint (LC) is an expression that may be written in the form a 1 x 1 +a 2 x 2 + · · · + a n x n op a 0 , where x i 's are numeric variables, a i 's  ... 
arXiv:2012.14366v1 fatcat:fzhrfpfkanbvth6kwzrwpxioa4

Computing Program Reliability Using Forward-Backward Precondition Analysis and Model Counting [chapter]

Aleksandar S. Dimovski, Axel Legay
2020 Lecture Notes in Computer Science  
In this work, we use a static analysis by abstract interpretation and model counting to construct probabilistic analysis of deterministic programs with uncertain input data, which can be used for estimating  ...  The obtained preconditions in the form of linear constraints are then analyzed to quantify how likely is an input to satisfy them.  ...  The analyses in [18, 17] address programs with integer domains and linear constraints, whereas the analyses in [3] address programs with linear and complex floating-point computations.  ... 
doi:10.1007/978-3-030-45234-6_9 fatcat:xky3vdtfn5gp3bw2a6fcj5bnki

The Application Potential of Integer Programming

Barry E. Cushing
1970 The journal of business  
Such problems may be too complex for a modeling approach, or may contain re- lationships which cannot be represented by linear functions, or may be character- ized by probabilistic relationships or per  ...  CUSHING* THE APPLICATION POTENTIAL OF INTEGER PROGRAMMING Linear programming has received much attention as a tool for managerial deci- sion making in business and government.  ... 
doi:10.1086/295309 fatcat:6zhprfi2tfen3ismlhzkzlk47i

Page 5548 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
) An algorithm for a class of nonlinear integer programming problems, and its convergence.  ...  In this paper these methods are applied to the following stochastic programs with probabilistic constraints: maximize c(x) subject to Pr{x € X: g;(x;z) > 0} > aj, 1<j<k, where z is a random vector on (  ... 
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