Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Cutting planes and column generation techniques with the projective algorithm
Journal of Optimization Theory and Applications
Linear controller design: limits of performance
Linear controller design: limits of performance
Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Rate-preserving discretization strategies for semi-infinite programming and optimal control
SIAM Journal on Control and Optimization
Control of uncertain systems: a linear programming approach
Control of uncertain systems: a linear programming approach
Robust and optimal control
Recent progress in unconstrained nonlinear optimization without derivatives
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Parameter Estimation in the Presence of Bounded Data Uncertainties
SIAM Journal on Matrix Analysis and Applications
Proximal methods in view of interior-point strategies
Journal of Optimization Theory and Applications
Mathematics of Operations Research
Computational Optimization and Applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Control: The Parametric Approach
Robust Control: The Parametric Approach
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Warm-Start Strategies in Interior-Point Methods for Linear Programming
SIAM Journal on Optimization
Reoptimization With the Primal-Dual Interior Point Method
SIAM Journal on Optimization
Approximating Subdifferentials by Random Sampling of Gradients
Mathematics of Operations Research
Robust portfolio selection problems
Mathematics of Operations Research
A robust minimax approach to classification
The Journal of Machine Learning Research
Operations Research
Convex Optimization
Solving convex programs by random walks
Journal of the ACM (JACM)
On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming
Mathematics of Operations Research
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
SIAM Journal on Optimization
Tractable Approximations to Robust Conic Optimization Problems
Mathematical Programming: Series A and B
An approximation technique for robust nonlinear optimization
Mathematical Programming: Series A and B
A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
Automatica (Journal of IFAC)
Nonlinear Optimization
SIAM Review
Robust minimum variance beamforming
IEEE Transactions on Signal Processing
On robust Capon beamforming and diagonal loading
IEEE Transactions on Signal Processing
Antenna array pattern synthesis via convex optimization
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Robust Beamforming via Worst-Case SINR Maximization
IEEE Transactions on Signal Processing
Fast Computation of Optimal Contact Forces
IEEE Transactions on Robotics
Robust solutions of uncertain linear programs
Operations Research Letters
Robust linear optimization under general norms
Operations Research Letters
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We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.