Related papers: EXPEDIS: An Exact Penalty Method over Discrete Set…
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
This paper aims to answer an open question recently posed in the literature, that is to find a fast exact method for solving the p-dispersion-sum problem (PDSP), a nonconcave quadratic binary maximization problem. We show that, since the…
We present MADAM, a parallel semidefinite based exact solver for Max-Cut, a problem of finding the cut with maximum weight in a given graph. The algorithm uses branch and bound paradigm that applies alternating direction method of…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact…
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method…