A stochastic halfspace projection method with flexible linearization point achieves O(1/sqrt(k)) optimality and feasibility violation for convex smooth objectives with nonsmooth constraints, and O(1/k) under strong convexity.
Tutorials on Advanced Optimization Methods
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abstract
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult (non-convex, multi-agent, min-max) problem to a solver-compatible form (semidefinite program, mixed-integer linear program) via convexification, linearization, and decomposition, so the original problem can be reliably solved by commercial/open-source software. Fundamental algorithms are not the main focus. This material is a good reference for self-learners who have basic knowledge in linear algebra and linear programming. It is one of the main references for an optimization course taught at Tsinghua University.
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Stochastic halfspace approximation method for convex optimization with nonsmooth functional constraints
A stochastic halfspace projection method with flexible linearization point achieves O(1/sqrt(k)) optimality and feasibility violation for convex smooth objectives with nonsmooth constraints, and O(1/k) under strong convexity.