Nonconvex Optimization for Statistical Estimation
Abstract
This research program aims to undertake a systematic investigation of nonconvexity andnondifferentiability in computational optimization with application to statistical estimation and extension to atypical stochastic programming .The focus will be onseveral classes of nonconvex, non-differentiable optimization problems:• a unified formulation of many statistical estimation problems as a composite difference-of-convex piecewise programs whose structures we will profitably exploit in undertaking the above-mentionedcomputational task and statistical analysis, including in particular the multi-layer neural networkproblems in deep learning;• optimization of an affine sparsity constraint system for the modeling of variable selection under logical conditions, comparing a soft formulation via a penalty term incorporated in the objective function with a hard formulation where the satisfaction of such constraints is strictly imposed;• optimization of nonconvex stochastics such as quantiles and risk measures of composite randomfunctionals, starting from the optimized certainty equivalent of a random variable, and itsspecial case of the well-known Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR); extension to the class of generalized deviation and risk measures as well as certain nonconvextwo-stage stochastic programs will also be considered.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 11, 2018
- Source ID
- FA95501810382
Entities
People
- Jong-shi Pang
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Southern California