A method for minimizing the sum of a convex function and a continuously differentiable function
Journal of Optimization Theory and Applications
Necessary conditions for optimal control of distributed parameter systems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications
Computational Optimization and Applications
SIAM Journal on Imaging Sciences
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Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints, are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to $L^1$-minimum norm control problems, $L^\infty$-norm minimization, and a class of optimal control problems with distributed state constraints and nonsmooth cost.