Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Logical analysis of numerical data
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Decision lists and related Boolean functions
Theoretical Computer Science
An Implementation of Logical Analysis of Data
IEEE Transactions on Knowledge and Data Engineering
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Design of Logic-based Intelligent Systems
Design of Logic-based Intelligent Systems
Pareto-optimal patterns in logical analysis of data
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques (Massive Computing)
Mathematical Programming: Series A and B
Integrated Methods for Optimization (International Series in Operations Research & Management Science)
Boolean Functions
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
A Sample Approximation Approach for Optimization with Probabilistic Constraints
SIAM Journal on Optimization
Pattern Theory: From Representation to Inference
Pattern Theory: From Representation to Inference
An integer programming approach for linear programs with probabilistic constraints
Mathematical Programming: Series A and B
Spanned patterns for the logical analysis of data
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
MIP reformulations of the probabilistic set covering problem
Mathematical Programming: Series A and B
On mixing sets arising in chance-constrained programming
Mathematical Programming: Series A and B
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We propose a new modeling and solution method for probabilistically constrained optimization problems. The methodology is based on the integration of the stochastic programming and combinatorial pattern recognition fields. It permits the fast solution of stochastic optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution and the generation of a consistent partially defined Boolean function pdBf representing the combination F,p of the binarized probability distribution F and the enforced probability level p. We show that the pdBf representing F,p can be compactly extended as a disjunctive normal form DNF. The DNF is a collection of combinatorial p-patterns, each defining sufficient conditions for a probabilistic constraint to hold. We propose two linear programming formulations for the generation of p-patterns that can be subsequently used to derive a linear programming inner approximation of the original stochastic problem. A formulation allowing for the concurrent generation of a p-pattern and the solution of the deterministic equivalent of the stochastic problem is also proposed. The number of binary variables included in the deterministic equivalent formulation is not an increasing function of the number of scenarios used to represent uncertainty. Results show that large-scale stochastic problems, in which up to 50,000 scenarios are used to describe the stochastic variables, can be consistently solved to optimality within a few seconds.