The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Quantifier elimination for formulas constrained by quadratic equations
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Algebraic numbers: an example of dynamic evaluation
Journal of Symbolic Computation
Applying quantifier elimination to the Birkhoff interpolation problem
Journal of Symbolic Computation
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Simulation and optimization by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
Improved projection for CAD's of R3
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares
SIAM Journal on Optimization
Applicable Algebra in Engineering, Communication and Computing
Computing the global optimum of a multivariate polynomial over the reals
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Proceedings of the 2009 conference on Symbolic numeric computation
Global optimization of polynomials using generalized critical values and sums of squares
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Theoretical Computer Science
A symbiosis of interval constraint propagation and cylindrical algebraic decomposition
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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With many applications in engineering and in scientific fields, quantifier elimination (QE) has been attracting more attention these days. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. We propose an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for solving polynomial optimization problems. The main ideas are a bounded CAD construction approach and utilization of sign information. The bounded CAD constructs CAD only in restricted admissible regions to remove redundant projection factors and avoid lifting cells where truth values are constant over the region. By utilization of sign information we can avoid symbolic computation in the lifting phase. Techniques for implementation are also presented. These techniques help reduce the computing time. We have examined our implementation by solving many example problems. Experimental results show that our implementation significantly improves efficiency compared to our previous work.