LEADER 02836nam 2200493 450 001 9910484421303321 005 20210312134500.0 010 $a3-030-61821-8 024 7 $a10.1007/978-3-030-61821-6 035 $a(CKB)4100000011728409 035 $a(DE-He213)978-3-030-61821-6 035 $a(MiAaPQ)EBC6461891 035 $a(PPN)253254256 035 $a(EXLCZ)994100000011728409 100 $a20210312d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvancing parametric optimization $eon multiparametric linear complementarity problems with parameters in general locations /$fNathan Adelgren 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (XII, 113 p. 8 illus., 7 illus. in color.) 225 1 $aSpringerBriefs in Optimization,$x2190-8354 311 $a3-030-61820-X 320 $aIncludes bibliographical references. 327 $a1. Introduction -- 2. Background on mpLCP -- 3. Algebraic Properties of Invariancy Regions -- 4. Phase 2: Partitioning the Parameter Space -- 5. Phase 1: Determining an Initial Feasible Solution -- 6. Further Considerations -- 7. Assessment of Performance -- 8. Conclusion -- Appendix A. Tableaux for Example 2.1 -- Appendix B. Tableaux for Example 2.2 -- References. 330 $aThe theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry. When unknown or uncertain data in an optimization problem is replaced with parameters, one obtains a multi-parametric optimization problem whose optimal solution comes in the form of a function of the parameters.The theory and methodology presented in this work allows one to solve both Linear Programs and convex Quadratic Programs containing parameters in any location within the problem data as well as multi-objective optimization problems with any number of convex quadratic or linear objectives and linear constraints. Applications of these classes of problems are extremely widespread, ranging from business and economics to chemical and environmental engineering. Prior to this work, no solution procedure existed for these general classes of problems except for the recently proposed algorithms. 410 0$aSpringerBriefs in Optimization,$x2190-8354 606 $aMathematical optimization 606 $aGeometry, Algebraic 615 0$aMathematical optimization. 615 0$aGeometry, Algebraic. 676 $a016.5192 700 $aAdelgren$b Nathan$01221184 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484421303321 996 $aAdvancing parametric optimization$92831544 997 $aUNINA