相关论文: A hybrid constraint programming and semidefinite p…
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…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
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…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
We discuss the issue of finding a good mathematical programming solver configuration for a particular instance of a given problem, and we propose a two-phase approach to solve it. In the first phase we learn the relationships between the…