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Research in Optimization and Equilibria
Main Research Thrusts: Professor Jong-Shi Pang
  • Global optimization of complementary convex programs
    • A complementary convex program (CCP) is a very challenging constrained optimization problem which is almost a convex program except for a special disjunctive constraint.  A major source of a CCP occurs in bi-level or inverse convex programming that includes the problem of parameter identification in convex minimization.  Our research focuses on the development of efficient algorithms to compute a globally optimal solution to a CCP if it exists and to provide a certificate otherwise.  Hierarchical decision making and cross validation in data mining are two areas where the methodology is being applied.


  • Computation of engineering and economic equilibria
    • Equilibrium is a pervasive phenomenon in engineering and economics.  The fundamental economic principle of supply balancing demand is a simple example of a market system in equilibrium.  The resolution of conflicts among multiple agents with selfish objectives requires the notion of an equilibrium of a game.  Our research focuses on the modeling, computation, and analysis of equilibrium problems arising from complex engineering and economics systems such as, electricity markets, communication networks, supply chains, oligopolistic production systems, and transportation.
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Research in Optimization and Equilibria (cont.)
Professor Jong-Shi Pang
  • Differential variational systems
    • Combining an ordinary differential equation with a finite-dimensional variational condition, a differential variational system is a novel mathematical paradigm that provides a broad framework for the modeling of complex dynamical systems containing unilateral constraints (in the form of algebraic inequalities) and disjunctions (yielding mode switches and state discontinuities).  Our research focuses on the analysis and control of such non-traditional dynamical systems and their optimization as well as applications to differential Nash games and dynamic traffic equilibrium problems.

  • Computational Financial Engineering
    • Financial engineering is a new discipline that pertains to the application of mathematical theory and engineering methods to the solution of financial decision making problems.  Portfolio selection and option pricing are two areas in financial engineering that require extensive optimization techniques and related numerical methods.  The proper quantification of risks is an important first step in formulating and solving a financial optimization problem.  The forward pricing of American and other exotic options and the inverse computation of implied volatilities from such prices are examples of research topics of interest to us.