Related papers: Stochastic Lipschitz Dynamic Programming
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
In this work, an adaptive time-stepping Milstein method is constructed for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift is one-sided Lipschitz continuous and the diffusion does not impose…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first…
In this paper, we extend the adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse to the multistage stochastic programming setting. The proposed algorithms integrate the adaptive partition-based…
We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their…
Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state…
This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point -- order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the…
We advance the state of the art in Mixed-Integer Linear Programming (MILP) formulations for Guillotine 2D Cutting Problems by (i) adapting a previously known reduction to our preprocessing phase and by (ii) enhancing a previous formulation…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints…
Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer…
In stochastic convex optimization problems, most existing adaptive methods rely on prior knowledge about the diameter bound $D$ when the smoothness or the Lipschitz constant is unknown. This often significantly affects performance as only a…
Two-stage stochastic mixed-integer programming (SMIP) problems with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing the subset of the…