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DOI: 10.23952/cot.2026.22
Received January 5, 2025; Accepted March 26, 2025; Published online February 17, 2026
Abstract. An optimal control problem is considered in which the control system is linear in the control variables and nonlinear in the state variables, with no control constraints. For this problem, we propose no-gap necessary and sufficient conditions for the weak minimality of a quadratic order which is the integral of the squared variation of an additional state variable. Here, the second variation is automatically degenerate, and we transform it to the classical possibly non-degenerate form that essentially simplifies verification of its sign definiteness.
How to Cite this Article:
A. Dmitruk, Second order conditions of the weak optimality for problems linear in the control, Commun. Optim. Theory 2026 (2026) 22.