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An integer programming approach for linear programs with probabilistic constraints

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. ...

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

*
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. ...

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

2004
*
Computers and Chemical Engineering
*

The paper begins

doi:10.1016/j.compchemeng.2003.09.017
fatcat:fzemoqbejvcdvgi5f34mpvw3lq
*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. ...##
###
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

2014
*
Environmental Systems Research
*

, interval-parameter

doi:10.1186/s40068-014-0015-9
fatcat:3gpvi2pobrg4znwlag55wq52am
*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 ...##
###
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

doi:10.21608/asc.2009.158225
fatcat:rkjwb5d5snbi7ph7nbmfvh6hma
*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 ...##
###
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

2013
*
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13
*

We propose

doi:10.1145/2491956.2462179
dblp:conf/pldi/SankaranarayananCG13
fatcat:5l7vkdhtgjhspn7r5ouitebhv4
*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. ...##
###
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]

2020
*
arXiv
*
pre-print

The

arXiv:2012.14366v1
fatcat:fzhrfpfkanbvth6kwzrwpxioa4
*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 ...##
###
Computing Program Reliability Using Forward-Backward Precondition Analysis and Model Counting
[chapter]

2020
*
Lecture Notes in Computer Science
*

In this work, we use a static analysis by abstract interpretation and model counting to construct

doi:10.1007/978-3-030-45234-6_9
fatcat:xky3vdtfn5gp3bw2a6fcj5bnki
*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. ...##
###
The Application Potential of Integer Programming

1970
*
The journal of business
*

Such problems may be too complex

doi:10.1086/295309
fatcat:6zhprfi2tfen3ismlhzkzlk47i
*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. ...##
###
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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