A barrier-type method for multiobjective optimization

References

• Carrizosa E, Frenk JBG. Dominating sets for convex functions with some applications. J Optim Theory Appl. 1998;96(2):281–295. doi: 10.1023/A:1022614029984
   Web of Science ®Google Scholar
• Eschenauer H, Koski J, Osyczka A. Multicriteria design optimization. Berlin: Springer; 1990.
   Google Scholar
• Sun Y, Ng DWK, Schober R. Multi-objective optimization for power efficient full-duplex wireless communication systems. 2015 IEEE Global Communications Conference; December; 2015. p. 1–6.
   Google Scholar
• Leschine TM, Wallenius H, Verdini WA. Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions. Eur J Oper Res. 1992;56(2):278–289. doi: 10.1016/0377-2217(92)90228-2
   Web of Science ®Google Scholar
• Tavana M. A subjective assessment of alternative mission architectures for the human exploration of Mars at NASA using multicriteria decision making. Comput Oper Res. 2004;31(7):1147–1164. doi: 10.1016/S0305-0548(03)00074-1
   Web of Science ®Google Scholar
• Gravel M, Martel JR, Nadeau R, et al. A multicriterion view of optimal resource allocation in job-shop production. Eur J Oper Res. 1992;61(1-2):230–244. doi: 10.1016/0377-2217(92)90284-G
   Web of Science ®Google Scholar
• White DJ. Epsilon-dominating solutions in mean–variance portfolio analysis. Eur J Oper Res. 1998;105(3):457–466. doi: 10.1016/S0377-2217(97)00056-8
   Web of Science ®Google Scholar
• Fu Y, Diwekar UM. An efficient sampling approach to multiobjective optimization. Ann Oper Res. 2004;132(1-4):109–134. doi: 10.1023/B:ANOR.0000045279.46948.dd
   Web of Science ®Google Scholar
• Fukuda EH, Graña Drummond LM. A survey on multiobjective descent methods. Pesq Oper. 2014;34(3):585–620. doi: 10.1590/0101-7438.2014.034.03.0585
   Google Scholar
• Bertsekas DP. Nonlinear programming. 3rd ed. Belmont (MA): Athena Scientific; 2016.
   Google Scholar
• Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming: theory and algorithms. 3rd ed. New York (NY): Wiley; 2006.
   Google Scholar
• Fliege J, Svaiter BF. Steepest descent methods for multicriteria optimization. Math Methods Oper Res. 2000;51(3):479–494. doi: 10.1007/s001860000043
   Web of Science ®Google Scholar
• Graña Drummond LM, Svaiter BF. A steepest descent method for vector optimization. J Comput Appl Math. 2005;175(2):395–414. doi: 10.1016/j.cam.2004.06.018
   Web of Science ®Google Scholar
• Graña Drummond LM, Iusem AN. A projected gradient method for vector optimization problems. Comput Optim Appl. 2004;28(1):5–29. doi: 10.1023/B:COAP.0000018877.86161.8b
   Web of Science ®Google Scholar
• Fukuda EH, Graña Drummond LM. On the convergence of the projected gradient method for vector optimization. Optimization. 2011;60(8-9):1009–1021. doi: 10.1080/02331934.2010.522710
   Web of Science ®Google Scholar
• Fukuda EH, Graña Drummond LM. Inexact projected gradient method for vector optimization. Comput Optim Appl. 2013;54(3):473–493. doi: 10.1007/s10589-012-9501-z
   Web of Science ®Google Scholar
• Fliege J, Graña Drummond LM, Svaiter BF. Newton's method for multiobjective optimization. SIAM J Optim. 2009;20(2):602–626. doi: 10.1137/08071692X
   Web of Science ®Google Scholar
• Graña Drummond LM, Raupp FMP, Svaiter BF. A quadratically convergent Newton method for vector optimization. Optimization. 2014;63(5):661–677. doi: 10.1080/02331934.2012.693082
   Web of Science ®Google Scholar
• Bonnel H, Iusem AN, Svaiter BF. Proximal methods in vector optimization. SIAM J Optim. 2005;15(4):953–970. doi: 10.1137/S1052623403429093
   Web of Science ®Google Scholar
• Chen Z, Huang XX, Yang XQ. Generalized proximal point algorithms for multiobjective optimization problems. Appl Anal. 2011;90(6):935–949. doi: 10.1080/00036811.2010.483428
   Web of Science ®Google Scholar
• Fukuda EH, Graña Drummond LM, Raupp FMP. An external penalty-type method for multicriteria. TOP. 2016;24(2):493–513. doi: 10.1007/s11750-015-0406-8
   Web of Science ®Google Scholar
• Jahn J. Vector optimization – theory, applications and extensions. Erlangen: Springer; 2003.
   Google Scholar
• Hiriart-Urruty JB, Lemaréchal C. Fundamentals of convex analysis. Heidelberg: Springer Verlag; 2001.
   Google Scholar
• Jahn J. Scalarization in vector optimization. Math Program. 1984;29(2):203–218. doi: 10.1007/BF02592221
   Web of Science ®Google Scholar
• Luc DT. Scalarization of vector optimization problems. J Optim Theory Appl. 1987;55(1):85–102. doi: 10.1007/BF00939046
   Web of Science ®Google Scholar