A Vector Problem of Optimal Control in a Hilbert Space

V. V. Gorokhovik, Convex and Nonsmooth Vector Optimization Problems [in Russian], Navuka i Tekhnika, Minsk (1990).

Q. J. Zhu, “Hamiltonian necessary conditions for a multiobjective optimal control problem with endpoint constraints,” SIAM J. Contr. Optim., 39, No.1, 97–112 (2001).

I. V. Sergienko, T. T. Lebedeva, and N. V. Semenova, “Existence of solutions in vector optimization problems,” Kibern. Sist. Anal., No. 6, 39–46 (2000).

T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Optimality and solvability conditions in linear vector optimization problems with a convex admissible set,” Dop. NAN Ukr., No. 10, 80–85 (2003).

Yu. M. Berezanskii, Expansion of Self-Adjoint Operators in Terms of Eigenfunctions [in Russian], Naukova Dumka, Kiev (1965).

S. I. Lyashko, Generalized Optimal Control of Linear Systems with Distributed Parameters, Kluwer, Boston (2002).

J.-L. Lions and E. Magenes, Problems aux limites non homogenes et applications [Russian translation], Mir, Moscow (1971).

B. Sh. Mordukhovich, Methods of Approximations in Optimization and Control Problems [in Russian], Nauka, Moscow (1988).

A. Ya. Dubovitskii and A. A. Milutin, “Extremum problems under constraints,” Dokl. AN SSSR, 149, No.4, 759–762 (1963).

J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations [Russian translation], Mir, Moscow (1972).

Chr. Tammer, “Approximate solutions of vector-valued control-approximation problems,” Studies in Locational Analysis, 10, 151–162 (1996).

P. Loridan, “ε-solutions in vector minimization problems,” J. of Optim. Theory and Appl., 43(2), 265–276 (1984).

Chr. Tammer, “A variational principle and applications for vectorial control approximation problems,” Rep. Inst. Optimizat. and Stochast., Martin-Luther Univ., Halle-Wittenberg (1996).

A. Gopfert, Chr. Tammer, and C. Zalinescu, “On the vectorial Ekeland’s variational principle and minimal points in product spaces,” Nonlinear Analysis. Theory, Methods & Appl. 39, 909–922 (2000).

J. Distel, Geometry of Banach Spaces [Russian translation], Vyshcha Shkola, Kiev (1980).

A. Hamel, “Suboptimal solutions of control problems for distributed parameter systems,” Rep. Inst. of Optimizat. and Stochast., Martin-Luther Univ., Halle-Wittenberg (1997).

V. V. Semenov, “Optimization of parabolic systems with conjugation conditions,” Dop. NAN Ukr., No. 5, 58–64 (2003).