This paper concerns the shortest path problem for a network in which arc costs can vary with time, each arc has a transit time, parking with a corresponding time-varying cost is allowed at the nodes, and time is modeled as a continuum. The resulting problem is called the continuoustime dynamic shortest path problem, which is well studied in the literature. However, the problem appears as a subp...

The literature in the eld of interior point methods for linear programming has been almost exclusively algorithm oriented. Recently G uler, Roos, Terlaky and Vial presented a complete duality theory for linear programming based on the interior point approach. In this paper we present a more simple approach which is based on an embedding of the primal problem and its dual into a skew symmetric ...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

The Fourier-Motzkin elimination method has been recently extended to linear inequality systems that have infinitely many inequalities. It has been used in the study of linear semi-infinite programming by Basu, Martin, and Ryan. Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang recently published in Optimization, which states “all the duality res...

In the last lecture we saw how to formulate a dual program for a linear program. From the formulation, it turned out that the dual program gave an upper/lower bound depending on whether the problem was maximization/minimization respectively. The strength of duality theory lies in the fact that these bounds are in fact tight. This implies that the dual value always agrees with the primal value. ...

We consider an extension of a linear model studied by Gale, Kuhn and Tucker (GKT) for an optimization problem with multiple criteria and multiple right-hand sides (resources), in which the constraints are nonlinear convex functions. We establish a strong duality result for the above model, of which the GKT result is a special case.

Dual linear programs are very useful to obtain bounds on the optimal value of the primal linear programs using the following two duality theorems. Theorem 1.1. Weak duality: Let x be a feasible solution for (P ) and y be a feasible solution for (D). Then, cx ≥ by. Theorem 1.2. Strong duality: For the linear programs in Figure 1, exactly one of the following possibilities occurs: 1. Both (P ) an...