Related papers: On Generating Lagrangian Cuts for Two-Stage Stocha…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
This study investigates imposing hard inequality constraints on the outputs of convolutional neural networks (CNN) during training. Several recent works showed that the theoretical and practical advantages of Lagrangian optimization over…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
Existing gradient coding schemes introduce identical redundancy across the coordinates of gradients and hence cannot fully utilize the computation results from partial stragglers. This motivates the introduction of diverse redundancies…
Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and…
We revisit the stochastic limited-memory BFGS (L-BFGS) algorithm. By proposing a new framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer…