Related papers: An Active Set Algorithm for Robust Combinatorial O…
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program. The first LP and…
We consider solving a combinatorial optimization problem with unknown knapsack constraints using a membership oracle for each unknown constraint such that, given a solution, the oracle determines whether the constraint is satisfied or not…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
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 work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
We introduce a general method for relaxing decision diagrams that allows one to bound job sequencing problems by solving a Lagrangian dual problem on a relaxed diagram. We also provide guidelines for identifying problems for which this…
In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…
We propose to generate Lagrangian cut for two-stage stochastic integer program by batch, in contrast to the existing methods which solve each Lagrangian subproblem at every iteration. We establish two convergence properties of the proposed…
Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…