Related papers: Addressing Unboundedness in Quadratically-Constrai…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…
The rapid evolution of machine learning (ML) has led to the widespread adoption of complex "black box" models, such as deep neural networks and ensemble methods. These models exhibit exceptional predictive performance, making them…
We investigate the computational complexity of min-max optimization under coupled constraints. The work of Daskalakis, Skoulakis, and Zampetakis [DSZ21] was the first to study min-max optimization through the lens of computational…
In high-dimensional classification settings, we wish to seek a balance between high power and ensuring control over a desired loss function. In many settings, the points most likely to be misclassified are those who lie near the decision…
Quality Diversity (QD) has emerged as a powerful alternative optimization paradigm that aims at generating large and diverse collections of solutions, notably with its flagship algorithm MAP-ELITES (ME) which evolves solutions through…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
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…
The two-dimensional non-oriented bin packing problem with due dates packs a set of rectangular items, which may be rotated by 90 degrees, into identical rectangular bins. The bins have equal processing times. An item's lateness is the…
Model Predictive Control has been recently proposed as policy approximation for Reinforcement Learning, offering a path towards safe and explainable Reinforcement Learning. This approach has been investigated for Q-learning and actor-critic…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…
Research on distributed machine learning algorithms has focused primarily on one of two extremes - algorithms that obey strict concurrency constraints or algorithms that obey few or no such constraints. We consider an intermediate…
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…
This paper discusses the computational resolution and presents numerical results for solving affine combinations of Heaviside composite optimization problems (abbreviated as A-HSCOPs) by a progressive integer programming (abbreviated as…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…