Related papers: Converging outer approximations to global attracto…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Consider a semidefinite program (SDP) involving an $n\times n$ positive semidefinite matrix $X$. The Burer-Monteiro method uses the substitution $X=Y Y^T$ to obtain a nonconvex optimization problem in terms of an $n\times p$ matrix $Y$.…
The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within 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…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
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…
To solve the separable convex optimization problem with linear constraints, Eckstein and Bertsekas introduced the generalized alternating direction method of multipliers (in short, GADMM), which is an efficient and simple acceleration…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
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…
We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means…
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…
Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein \& Bertsekas [Math. Prog., 1992] has inspired intensive attention in analyzing its theoretical…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…