相关论文: Exploiting Semidefinite Relaxations in Constraint …

In most constraint programming systems, a limited number of search engines is offered while the programming of user-customized search algorithms requires low-level efforts, which complicates the deployment of such algorithms. To alleviate…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

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…

Many clustering problems enjoy solutions by semidefinite programming. Theoretical results in this vein frequently consider data with a planted clustering and a notion of signal strength such that the semidefinite program exactly recovers…

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

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…

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 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…

We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…

To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large semidefinite programs tend to be computationally challenging.…

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…

Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver…

We consider the problem of learning decision rules for prediction with feature budget constraint. In particular, we are interested in pruning an ensemble of decision trees to reduce expected feature cost while maintaining high prediction…

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…

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…