Related papers: An Outer Approximation Method for Solving Mixed-In…
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
In this paper, we present a distributed algorithm utilizing the proximal alternating direction method of multipliers (ADMM) in conjunction with sequential constraint tightening to address mixed-integer quadratic programming (MIQP) problems…
Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
In this work, we propose an outer approximation algorithm for solving bounded convex vector optimization problems (CVOPs). The scalarization model solved iteratively within the algorithm is a modification of the norm-minimizing…
Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…
We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…
Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for…
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…
This paper presents the Distributed Primal Outer Approximation (DiPOA) algorithm for solving Sparse Convex Programming (SCP) problems with separable structures, efficiently, and in a decentralized manner. The DiPOA algorithm development…
The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It…
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
Mixed integer linear programming (MILP) has seen a sharp rise in use for engineering optimization applications in recent years. Even for initially non-linear problems, it is often the method of choice. Then, the non-linear functions have to…