The topic of this thesis, integer and combinatorial optimization, involves minimizing (or maximizing) a function of many variables, some of which belong to a discrete set, subject to constraints. This area has abundant applications in industry. Integer and combinatorial optimization problems are often difficult to solve due to the large and complex set of alternatives. The objective of this the...

We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.

Recently, there has been a significant interest in introducing stochastic dominance relations as constraints into stochastic optimization problems. Optimization with first order stochastic dominance constraints in discrete distribution case can be formulated as mixed integer programs. In this article, we present a method to safely approximate such kinds of mixed integer programs. © 2009 World A...

We study the existence of integer solutions to max-linear optimization problems. Specifically, we show that, in a generic case, the integer max-linear optimization problem can be solved in strongly polynomial time. This extends results from our previous papers where polynomial methods for this generic case were given.

Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted p...

We study the problem of minimizing a convex function on nonempty, finite subset integer lattice when cannot be evaluated at noninteger points. propose new underestimator that does not require access to (sub)gradients objective; such information is unavailable objective blackbox function. Rather, our uses secant linear functions interpolate previously These mappings are shown underestimate in di...

For many years the mathematical programming community has realized the practical importance of developing algorithmic tools for tackling mixed integer optimization problems. Given our ability to solve linear optimization problems efficiently, one is inclined to think that a mixed integer program with both continuous and discrete variables is easier than a pure integer programming problem since ...