Results 1  10
of
65
Universally Quantified Interval Constraints
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decompo ..."
Abstract

Cited by 46 (0 self)
 Add to MetaCart
Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of innerapproximation of real relations.
Novel Approaches to Numerical Software with Result Verification
 NUMERICAL SOFTWARE WITH RESULT VERIFICATION, INTERNATIONAL DAGSTUHL SEMINAR, DAGSTUHL
, 2003
"... Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦¨§� © ©���� £��������� � that transforms input © ©�� into �� � £��������� � ©���� the output, and we £��������� � know the intervals of possible values of the inputs. Many real ..."
Abstract

Cited by 26 (18 self)
 Add to MetaCart
Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦¨§� © ©���� £��������� � that transforms input © ©�� into �� � £��������� � ©���� the output, and we £��������� � know the intervals of possible values of the inputs. Many reallife problems go beyond this paradigm. In some cases, we do not have an algorithm ¦, we only know some relation (constraints) between ©� � and. In other cases, in addition to knowing the intervals, we may know some relations between; we may have some information about the probabilities of different values of © � , and we may know the exact values of some of the inputs (e.g., we may know that © £ ���¨�� �). In this paper, we describe the approaches for solving these reallife problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.
Efficient solving of quantified inequality constraints over the real numbers
 ACM Transactions on Computational Logic
"... Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In the ..."
Abstract

Cited by 25 (7 self)
 Add to MetaCart
Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques. 1
Continuous FirstOrder Constraint Satisfaction
 ARTIFICIAL INTELLIGENCE, AUTOMATED REASONING, AND SYMBOLIC COMPUTATION, NUMBER 2385 IN LNCS
, 2002
"... This paper shows how to use constraint programming techniques for solving firstorder constraints over the reals (i.e., formulas in the firstorder predicate language over the structure of the real numbers). More specifically, based on a narrowing operator that implements an arbitrary notion of con ..."
Abstract

Cited by 22 (12 self)
 Add to MetaCart
This paper shows how to use constraint programming techniques for solving firstorder constraints over the reals (i.e., formulas in the firstorder predicate language over the structure of the real numbers). More specifically, based on a narrowing operator that implements an arbitrary notion of consistency for atomic constraints over the reals (e.g., boxconsistency), the paper provides a narrowing operator for firstorder constraints that implements a corresponding notion of firstorder consistency, and a solver based on such a narrowing operator. As a consequence, this solver can take over various favorable properties from the field of constraint programming.
Guaranteed Nonlinear Estimation Using Constraint Propagation on Sets
, 2001
"... Boundederror estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitabl y de...ned errors shoul d bel ong to some prior feasibl e sets. When the model outputs arel inear in the vector to be estimated, a number of methods a ..."
Abstract

Cited by 22 (12 self)
 Add to MetaCart
Boundederror estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitabl y de...ned errors shoul d bel ong to some prior feasibl e sets. When the model outputs arel inear in the vector to be estimated, a number of methods are avail#0 l e to encl ose al# estimates that are consistent with the data into simpl# sets such as el# ipsoids, orthotopes or paral#0xP90O es, thereby providing guaranteed set estimates. In the nonl#x]30 case, the situation is muchl#O4 devel#O ed and there are very few methods that produce such guaranteed estimates. In this paper, the discretetime probl em is cast into the more general framework of constraint satisfaction probl ems.Al# orithms rathercl assical in the area of interval constraint propagation are extended by repl acing interva l# by moregeneral subsets of real vector spaces. This makes it possibl# to propose a new al#9Oq30 m that contracts the feasibl e domains for each uncertain variabl# optimal#O (i.e., no smal# er domain coul d be obtained) and ecientl# . The resul ting methodol#03 isil#34 trated on discretetime nonl#O0O7 state estimation. The state at time k is estimated either from past measurement onl y or from al l measurements assumed to be avai l#bl# from the start. Even in the causal case, prior information on the future val# e of the state and output vectors, due for instance to physical constraints, is readil y taken into account.
Efficient and safe global constraints for handling numerical constraint systems
 SIAM J. NUMER. ANAL
, 2005
"... Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies, and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies, and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints. Then, it introduces a generalization of Quad to polynomial constraint systems. It also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system. Different linearization techniques are investigated to limit the number of generated constraints. QuadSolver, a new branch and prune algorithm that combines Quad, local consistencies, and interval methods, is introduced. QuadSolver has been evaluated on a variety of benchmarks from kinematics, mechanics, and robotics. On these benchmarks, it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with stateoftheart optimization solvers.
Contractor Programming
 Artificial Intelligence
"... Abstract. This paper describes a solver programming method, called contractor programming, that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restr ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
Abstract. This paper describes a solver programming method, called contractor programming, that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restricting users to choose among a list of fixed strategies. Our first contribution is to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available. Programming consists in applying operators (intersection, composition, etc.) on algorithms called contractors that are somehow similar to propagators. Second, many problems with real variables cannot be cast as the search for vectors simultaneously satisfying the set of constraints, but a large variety of different outputs may be demanded from a set of constraints (e.g., a paving with boxes inside and outside of the solution set). These outputs can actually be viewed as the result of different contractors working concurrently on the same search space, with a bisection procedure intervening in case of deadlock. Such algorithms (which are not strictly speaking solvers) will be made easy to build thanks to a new branch & prune system, called paver. Thus, this paper gives a way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms. The contractor formalism and the paver system are the two contributions. The approach is motivated and justified through different cases of study. An implementation of this framework named Quimper is also presented. 1
Using Directed Acyclic Graphs to Coordinate Propagation and Search for Numerical Constraint Satisfaction Problems
 In Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2004
, 2004
"... A. NEUMAIER [1] has given the fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation. We show in this paper how constraint propagation on DAGs can be made efficient and practical by: (i) working on partial DAG representations; and (ii) ..."
Abstract

Cited by 14 (5 self)
 Add to MetaCart
A. NEUMAIER [1] has given the fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation. We show in this paper how constraint propagation on DAGs can be made efficient and practical by: (i) working on partial DAG representations; and (ii) enabling the flexible choice of the interval inclusion functions during propagation. We then propose a new simple algorithm which coordinates constraint propagation and exhaustive search for solving numerical constraint satisfaction problems. The experiments carried out on different problems show that the new approach outperforms previously available propagation techniques by an order of magnitude or more in speed, while being roughly the same quality w.r.t. enclosure properties. I.
RealPaver: An Interval Solver using Constraint Satisfaction Techniques
 ACM TRANS. ON MATHEMATICAL SOFTWARE
, 2006
"... RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed, using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreove ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed, using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or non square, sparse or dense, linear, polynomial or involving transcendental functions. The modeling language permits stating constraint models and tuning parameters of solving algorithms, which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, 3B) are implemented. The distribution includes C sources, executables for different machine architectures, documentation and benchmarks. The portability is ensured by the GNU C compiler.
Interval Constraint Solving for Camera Control and Motion Planning
 Bell Northern Research
, 2004
"... Many problems in robust control and motion planning can be reduced to either find a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the “guaranteed tuning problem ” as defined by Jaulin and Walter, which amounts to finding a value for some tuning parame ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Many problems in robust control and motion planning can be reduced to either find a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the “guaranteed tuning problem ” as defined by Jaulin and Walter, which amounts to finding a value for some tuning parameter such that a set of inequalities be verified for all the possible values of some perturbation vector. A classical approach to solve these problems, which satisfies the strong soundness requirement, involves some quantifier elimination procedure such as Collins ’ Cylindrical Algebraic Decomposition symbolic method. Sound numerical methods using interval arithmetic and local consistency enforcement to prune the search space are presented in this paper as much faster alternatives for both soundly solving systems of nonlinear inequalities, and addressing the guaranteed tuning problem whenever the perturbation vector has dimension one. The use of these methods in camera control is investigated, and experiments with the prototype of a declarative modeller to express camera motion using a cinematic language are reported and commented.