References
- Ehrgott M Multicriteria optimization. Berlin: Springer Science & Business Media; 2005.
- Jahn J. Vector optimization. Berlin: Springer; 2009.
- Liu GP, Yang JB, Whidborne JF. Multiobjective optimisation and control. Research Studies Press; 2003.
- Marler RT, Arora JS. Survey of multi-objective optimization methods for engineering. Struct Multidiscipl Optim. 2004;26(6):369–395.
- Liu W, Gong W, Yan N. A new finite element approximation of a state-constrained optimal control problem. J Comput Math. 2009;27(1):97–114.
- Meyer C. Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints. Control Cybern. 2008;37(1):51–83.
- Deckelnick K, Hinze M. Convergence of a finite element approximation to a state-constrained elliptic control problem. SIAM J Numer Anal. 2007;45(5):1937–1953.
- Merino P, Neitzel I, Tröltzsch F. On linear-quadratic elliptic control problems of semi-infinite type. Appl Anal. 2011;90(6):1047–1074.
- Merino P, Neitzel I, Tröltzsch F. An adaptive numerical method for semi-infinite elliptic control problems based on error estimates. Optim Methods Softw. 2015;30(3):492–515.
- Neitzel I, Tröltzsch F. Numerical analysis of state-constrained optimal control problems for pdes. In: Constrained optimization and optimal control for partial differential equations. Springer; 2012. p. 467–482.
- Beermann D, Dellnitz M, Peitz S, et al. Pod-based multiobjective optimal control of pdes with non-smooth objectives. PAMM. 2017;17(1):51–54.
- Beermann D, Dellnitz M, Peitz S, et al. Set-oriented multiobjective optimal control of pdes using proper orthogonal decomposition. In: Reduced-order modeling (rom) for simulation and optimization. Springer; 2018. p. 47–72.
- Peitz S, Dellnitz M. A survey of recent trends in multiobjective optimal control–surrogate models, feedback control and objective reduction. Math Comput Appl. 2018;23(2):30.
- Iapichino L, Ulbrich S, Volkwein S. Multiobjective PDE-constrained optimization using the reduced-basis method. Adv Comput Math. 2017;43(5):945–972.
- Christof C, Müller G. Multiobjective optimal control of a non-smooth semilinear elliptic partial differential equation. European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimisation and Calculus of Variations; 2020.
- Schiel R. Vector optimization and control with partial differential equations and pointwise state constraints [dissertation]. FAU Erlangen-Nürnberg; 2014.
- Hintermüller M, Kunisch K. Path-following methods for a class of constrained minimization problems in function space. SIAM J Optim. 2006;17(1):159–187.
- Schiela A. Barrier methods for optimal control problems with state constraints. SIAM J Optim. 2009;20(2):1002–1031.
- Rösch A, Tröltzsch F. Existence of regular lagrange multipliers for a nonlinear elliptic optimal control problem with pointwise control-state constraints. SIAM J Control Optim. 2006;45(2):548–564.
- Khan AA, Sama M. A new conical regularization for some optimization and optimal control problems: convergence analysis and finite element discretization. Numer Funct Anal Optim. 2013;34(8):861–895.
- Jadamba B, Khan AA, Sama M. Regularization for state constrained optimal control problems by half spaces based decoupling. Syst Control Lett. 2012;61(6):707–713.
- Lopez R, Sama M. Stability and sensivity analysis for conical regularization of linearly constrained least-squares problems in hilbert spaces. J Math Anal Appl. 2017;456(1):476–495.
- Jadamba B, Khan A, Sama M. Error estimates for integral constraint regularization of state-constrained elliptic control problems. Comput Optim Appl. 2017;67(1):39–71.
- Jadamba B, Khan AA, Sama M. Stable conical regularization by constructible dilating cones with an application to Lp-constrained optimization problems. Taiwan J Math. 2019;23(4):1001–1023.
- Huerga L, Jadamba B, Sama M. An extension of the kaliszewski cone to non-polyhedral pointed cones in infinite-dimensional spaces. J Optim Theory Appl. 2019;181(2):437–455.
- Huerga L, Khan A, Sama M. A henig conical regularization approach for circumventing the slater conundrum in linearly ℓ+p-constrained least squares problems. J Appl Numer Optim. 2019;1(2):117–129.
- Jadamba B, Khan AA, López R, et al. Conical regularization for multi-objective optimization problems. J Math Anal Appl. 2019;479(2):2056–2075.
- Casas E, Mateos M. Numerical approximation of elliptic control problems with finitely many pointwise constraints. Comput Optim Appl. 2012;51(3):1319–1343.
- Leykekhman D, Meidner D, Vexler B. Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints. Comput Optim Appl. 2013;55(3):769–802.
- Casas E. Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. ESAIM Control Optim Calc Var. 2002;8:345–374.
- Liu W, Yang D, Yuan L, et al. Finite element approximations of an optimal control problem with integral state constraint. SIAM J Numer Anal. 2010;48(3):1163–1185.
- Mosco U. Convergence of convex sets and of solutions of variational inequalities. Adv Math. 1969;3(4):510–585.
- Ekeland I, Temam R. Convex analysis and variational problems. Philadelphia: SIAM; 1999.
- Hinze M, Meyer C. Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems. Comput Optim Appl. 2010;46(3):487–510.
- Megginson RE. An introduction to Banach space theory. New York: Springer-Verlag; 1998.
- Casas E. Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM Journal on Control and Optimization. 1993;31(4):993–1006.
- Alibert JJ, Raymond JP. Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. Numer Funct Anal Optim. 1997;18(3-4):235–250.
- Tröltzsch F. Optimal control of partial differential equations. Providence (RI): American Mathematical Society; 2010.
- Gessesse HE, Troitsky VG. Invariant subspaces of positive quasinilpotent operators on ordered banach spaces. Positivity. 2008;12(2):193–208.
- Brenner SC, Scott LR. The mathematical theory of finite element methods. New York: Springer; 2008.
- Grisvard P. Elliptic problems in nonsmooth domains. Pitman: Advanced Publishing Program; 1985.
- Maz'ya V, Rossmann J. Elliptic equations in polyhedral domains. Providence (RI): American Mathematical Society, Vol. 162; 2010. p. viii+608 (Mathematical Surveys and Monographs).
- Guzmán J, Leykekhman D, Rossmann J, et al. Hölder estimates for Green's functions on convex polyhedral domains and their applications to finite element methods. Numer Math. 2009;112(2):221–243.
- Davydov O. Approximation by piecewise constants on convex partitions. J Approx Theory. 2012;164(2):346–352.
- Tanino T. Stability and sensitivity analysis in convex vector optimization. SIAM J Control Optim. 1988;26(3):521–536.
- Shi D. Contingent derivative of the perturbation map in multiobjective optimization. J Optim Theory Appl. 1991;70(2):385–396.
- Luc DT, Soleimani-Damaneh M, Zamani M. Semi-differentiability of the marginal mapping in vector optimization. SIAM J Optim. 2018;28(2):1255–1281.
- An DTV, Gutiérrez C. Differential stability properties in convex scalar and vector optimization. Set-Valued Var Anal. 2021;29:893–914.
- Hinze M, Schiela A. Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment. Comput Optim Appl. 2011;48(3):581–600.
- Khan A, Sama M. Stability analysis of conically perturbed linearly constrained least-squares problems by optimizing the regularized trajectories. Optim Lett. 2021;15:2127–2145.