Related papers: On Generalized Surrogate Duality in Mixed-Integer …
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility…
For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semidefinite programming (SDP) relaxation…
In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse…
This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
This paper presents a comprehensive theoretical analysis of six distinct Mixed-Integer Programming (MIP) formulations for preventive Generator Maintenance Scheduling (GMS), a critical problem for ensuring the reliability and efficiency of…
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix…
This paper presents a solver-friendly logic-based mixed-integer nonlinear programming model (LB-MINLP) to solve economic dispatch (ED) problems considering disjoint operating zones and valve-point effects. A simultaneous consideration of…
We consider the problem of maximizing a convex quadratic function over a bounded polyhedral set. We design a new framework based on SDP relaxations and cutting plane methods for solving the associated reference value problem. The major…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
We propose a novel edge computing network architecture that enables edge nodes to cooperate in sharing computing and radio resources to minimize the total energy consumption of mobile users while meeting their delay requirements. To find…
We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…
In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide…