Dr. Dentcheva’s current research is associated with stochastic optimization models with stochastic dominance constraints and risk functions. Along with Andrzej Ruszczyski, Rutgers University, she has introduced a new type of optimization models constraining risk, which involve stochastic orders and risk functions. These problems are not only practically relevant but represent a mathematical challenge because they are nonlinear and non-smooth with respect to the decisions and nonlinear in probability. Stochastic ordering constrains generally result in semi-infinite optimization problems.
She has also worked on probabilistically constrained stochastic optimization models with several collaborators, including Andras Prékopa from Rutgers University, and one of her graduate students. They have developed optimality conditions for nonlinear problems involving random vectors as right hand site of constraints and proposed a novel solution methodology based on duality and non-smooth optimization.
Dr. Dentcheva has analyzed stability and sensitivity of stochastic optimization problems, and obtained second-order differentiability of optimal values and differentiability properties of solutions for two-stage stochastic optimization problems. Another topic she has worked on is the analysis of decomposition methods for discrete and non-convex stochastic optimization problems. She has established general relations among these methods with respect to their duality gaps.
She is the director of the graduate program Analysis and Optimization of Stochastic Systems, which is a unique interdisciplinary graduate program providing solid and rigorous education in the area of analysis and optimization of complex stochastic systems under uncertainty and risk. The program combines statistical analysis with modern decision methods such as stochastic optimization and control, models of risk, and game theory.
Dr. Dentcheva is also the Associate Editor of SIAM Journal on Optimization and a member of Society of Industrial and Applied Mathematics. In addition, she is a reviewer for Mathematical Reviews and a member of the American Mathematical Society, past member of the Stochastic Programming Committee of the Mathematical Programming Society, and the Union of Bulgarian Mathematicians.
She has received honors and awards such as the Davis Memorial Research Award 2007 for excellence in research, several NSF awards, as well as the DAAD (Deutsche Akademische Austausch Dienst) and Deutsche Forschungsgemeinschaft award.