On the identification of active constraints
SIAM Journal on Numerical Analysis
Finite termination of the proximal point algorithm
Mathematical Programming: Series A and B
Identifiable surfaces in constrained optimization
SIAM Journal on Control and Optimization
Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
First and second order analysis of nonlinear semidefinite programs
Mathematical Programming: Series A and B
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
SIAM Journal on Optimization
Active Sets, Nonsmoothness, and Sensitivity
SIAM Journal on Optimization
Constraint nondegeneracy in variational analysis
Mathematics of Operations Research
Typical convex program is very well posed
Mathematical Programming: Series A and B
A **-algorithm for convex minimization
Mathematical Programming: Series A and B
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Mathematics of Operations Research
Semidefinite representation of convex sets
Mathematical Programming: Series A and B
An Invitation to Tame Optimization
SIAM Journal on Optimization
Identifying Structure of Nonsmooth Convex Functions by the Bundle Technique
SIAM Journal on Optimization
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We consider linear optimization over a nonempty convex semialgebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique “active” manifold, around which F is “partly smooth,” and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.