Related papers: Convex mixed integer nonlinear programming problem…
For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these…
In this paper, we mainly study one class of mixed-integer nonlinear programming problems (MINLPs) with vector conic constraint in Banach spaces. Duality theory of convex vector optimization problems applied to this class of MINLPs is deeply…
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…
Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has…
Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…
A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic…
We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
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 study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…
Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with…
In this work, we aim to compare different methods and formulations to solve a problem in air traffic management to global optimality. In particular, we focus on the aircraft deconfliction problem, where we are given n aircraft, their…
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…
The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…