相关论文: A hybrid constraint programming and semidefinite p…

Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…

This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…

In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a…

We first formulate the problem of optimally scheduling air traffic low with sector capacity constraints as a mixed integer linear program. We then use semidefinite relaxation techniques to form a convex relaxation of that problem. Finally,…

Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…

The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

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…

In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…

This paper deals with the maximum independent set (M.I.S.) problem, also known as the stable set problem. The basic mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables $x_j$ and…

We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…

Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is…

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…

Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…

In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a…

In this paper, we propose an effective search procedure that interleaves two steps: subproblem generation and subproblem solution. We mainly focus on the first part. It consists of a variable domain value ranking based on reduced costs.…

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions…

This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…

This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…