In this paper, we consider the Forward–Backward proximal splitting algorithm to minimize the sum of two proper closed convex functions, one of which having a Lipschitz–continuous gradient and the other being partly smooth relatively to an active manifold $\mathcal{M}$. We propose a unified framework in which we show that the Forward–Backward (i) correctly identifies the … Read more
Optimization problems with cardinality constraints are very dicult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also discussed in … Read more
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art performance. … Read more
The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of … Read more
Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing … Read more
We propose two new Lagrangian dual problems for chance-constrained stochastic programs based on relaxing nonanticipativity constraints. We compare the strength of the proposed dual bounds and demonstrate that they are superior to the bound obtained from the continuous relaxation of a standard mixed-integer programming (MIP) formulation. For a given dual solution, the associated Lagrangian relaxation … Read more
Many dynamic decision problems involving uncertainty can be appropriately modeled as multi-stage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of Sandikci et al. (2013) on two-stage stochastic mixed-integer-programs (SMIPs), this paper develops … Read more
In this work we propose, analyze, and test algorithms for linearly constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, … Read more
In this article, six different mixed integer programming (MIP) formulations are proposed and analyzed. These formulations are based on the knowledge of four different paradigms for single machine scheduling problems (SMSP) with sequence dependent setup times and release dates. Each formulation reflects a specific concept on how the variables and parameters are defined, requiring particular … Read more
In Pareto bi-objective integer optimization the optimal result corresponds to a set of non- dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team orienteering problem with … Read more