ARTICLES/RESEARCH QUESTIONS/LECTURES

Organized by date

EQUILIBRIUM

• STABILITY & CONVERGENCE OF BIVARIATE FUNCTIONS
• Stability of equilibrium points II
• Variational convergence of bivariate functions: Motivating applications II
• Variational convergence of bivariate functions: Motivating applications I
• Variational convergence of bivariate functions: Theoretical foundations
• Variational Convergence of Bivariate Functions
• Stability of equilibrium points
• Continuity properties of Walras equilibrium points
• DETERMINISTIC: COMPUTATIONAL SCHEMES
• Variational inequalities and economic equilibrium
• A variational inequality scheme for determining an economic equilibrium of classical or extended type
• EQUILIBRIUM IN A STOCHASTIC ENVIRONMENTS & STOCHASTIC GAMES
• Equilibrium in a stochastic environment: a `constructive' approach
• Non-Cooperative games in a stochastic environment

STATISTICAL ESTIMATION

• POOR DATA ISSUES
• Density estimation: exploiting non-data information
• Statistical Estimation: Data and Non-Data Information
• Statistical estimation from an optimization viewpoint
• Estimating density functions: a constrained maximum likelihood approach
• Constrained estimation: consistency and asymptotics
• PROBABILISTIC FOUNDATIONS
• Random lsc functions: an Ergodic Theorem
• Random lsc functions: Scalarization
• Random closed sets and random lsc functions: Kolmogorov's extension theorem
• Epigraphical processes: laws of large numbers for random lsc functions
• Convergence of probability measures revisited
• INTERFACE WITH STOCHASTIC PROGRAMMING MODELS
• An ergodic theorem for stochastic programming problems
• Epi-consistency of convex stochastic programs
• Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems

VARIATIONAL ANALYSIS

• VARIATIONAL ANALYSIS (2nd Edition) Published by Springer
• ARTICLES
• Lipschitz continuity of inf-projections
• Convergence of set-valued mappings: Equi-outer semicontinuity
• The facets of the polyhedral set determined by the Gale-Hoffman inequalities
• Epigraphical analysis
• Continuity of some convex-cone-valued mappings

STOCHASTIC PROGRAMMING

• OVERVIEW
• Making Stochastic Programming User-Friendly
• Dealing with Uncertainty in Decision Making Models
• Stochastic dynamic optimization: Approaches and computation
• APPLICATIONS
• Stochastic optimization for lake eutrophication management
• On an approach to optimization problems with probabilistic cost and or constraints
• NUMERICAL SCHEMES
• A dual strategy for the implementation of the aggregation principle in decision making under uncertainty
• A class of stochastic programs with decision dependent random elements
• Scenarios and policy aggregation in optimization under uncertainty
• Solving stochastic programs with simple recourse
• THEORY (mostly stability issues)
• Stability of 'epsilon'-approximate solutions to convex stochastic programs
• Stochastic programming models: wait-and-see versus here-and-now
• Stochastic programs with chance constraints: Generalized convexity and approximation issues
• Consistency of minimizers and the SLLN for stochastic programs
• Stability results for stochastic programs and sensors, allowing for discontinuous objective functions

MATHEMATICAL FINANCE

• MARKET STRUCTURE
• Term and volatility structures
• EpiCurves
• Serious zero-curves
• PRICING FINANCIAL INSTRUMENTS
• Pricing contingent claims: a computational compatible approach
• Pricing arbitrary fixed income with short rate trees

POLYHEDRAL MAPPINGS: CONTINUITY

• POSITIVE HULL MAPPINGS
• Continuity of positive hull mappings with application to semi-infinite and stochastic programming
• Continuity of some convex-cone-valued mappings
• EpiCurves
• POLYHEDRAL MAPPINGS
• A Lipschitzian characterization of convex polyhedra
• On the continuity of the value of a linear program and related polyhedral functions

TEXTBOOK -- LECTURES NOTES

• AN OPTIMIZATION PRIMER

TESTIMONIALS

• Foreword to Special issue of Mathematical Programming: "Variational Analysis, Optimization and their Applications" (Festschrift for R.T. Rockafellar's 70th birthday)
• Celabrating Dantzig's 90th and Cottle and Veinott's 70th