相关论文: Extended Triangle Inequalities for Nonconvex Box-C…

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth…

Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…

Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…

Constraints solvers play a significant role in the analysis, synthesis, and formal verification of complex embedded and cyber-physical systems. In this paper, we study the problem of designing a scalable constraints solver for an important…

This note uses the Total Least-Squares (TLS) line-fitting problem as a canvas to explore some modern optimization tools. The contribution is meant to be tutorial in nature. The TLS problem has a lot of mathematical similarities to important…

It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…

An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…

Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control systems. Nevertheless, the…

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing…

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…

We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x - c\| \le b^T x - a$. In…

This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive real and complex solutions for the RBLSE problem by utilizing…

Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…

We study geometric characterizations of unbounded integer polynomial optimization problems. While unboundedness along a ray fully characterizes unbounded integer linear and quadratic optimization problems, we show that this is not the case…

In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is…

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…

We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…