Minimum cost flow problems in infinite networks arise, for example, in infinite-horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for the special case of linear costs using an infinite-dimensional simplex algorithm. Here, we use a different approach to derive duality results when the costs are convex. We formulate the pr...

Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states’ longterm value under a given policy. In this paper, we focus on policy evaluation with linear function approximation over a fixed dataset. We first transform the empirical policy evaluation problem into a (quadratic) convex-concave saddle point problem, and then ...

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

It is well known that the standard BDDC algorithm [1] requires a strong assumption on coefficients of the model problem related to the subdomain partition to achieve a good performance. In the works by Clemense and Scheichl [2,3], a bound of condition number of FETI algorithms has been analyzed depending on the coefficient variations inside subdomains. A similar problem was also considered in t...

In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results...

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pu...

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.