SIAM Journal on Control and Optimization
Optimality Conditions for a Constrained Control Problem
SIAM Journal on Control and Optimization
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Weak maximum principle for optimal control problems with mixed constraints
Nonlinear Analysis: Theory, Methods & Applications
Optimal Control Problems with Set-Valued Control and State Constraints
SIAM Journal on Optimization
Optimality Conditions: Abnormal and Degenerate Problems (Mathematics and its Applications Volume 526)
Necessary Conditions for Constrained Problems under Mangasarian-Fromowitz Conditions
SIAM Journal on Control and Optimization
An Extension of the Schwarzkopf Multiplier Rule in Optimal Control
SIAM Journal on Control and Optimization
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We develop necessary conditions of broad applicability for optimal control problems in which the state and control are subject to mixed constraints. We unify, subsume, and significantly extend most of the results on this subject, notably in the three special cases that comprise the bulk of the literature: calculus of variations, differential-algebraic systems, and mixed constraints specified by equalities and inequalities. Our approach also provides a new and unified calibrated formulation of the appropriate constraint qualifications, and shows how to extend them to nonsmooth data. Other features include a very weak hypothesis concerning the type of local minimum, nonrestrictive hypotheses on the data, and stronger conclusions, notably as regards the maximum (or Weierstrass) condition. The necessary conditions are stratified, in the sense that they are asserted on precisely the domain upon which the hypotheses (and the optimality) are assumed to hold. This leads to local, intermediate, and global versions of the necessary conditions, according to how the hypotheses are formulated.