Related papers: Exact Optimization: Part I
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of…
In this paper, we delve into the statistical analysis of the fitted Q-evaluation (FQE) method, which focuses on estimating the value of a target policy using offline data generated by some behavior policy. We provide a comprehensive…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show…
Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We present a new framework for solving optimization problems with a diseconomy of scale. In such problems, our goal is to minimize the cost of resources used to perform a certain task. The cost of resources grows superlinearly, as $x^q$,…
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the…
We study the Bipartite Unconstrained 0-1 Quadratic Programming Problem (BQP) which is a relaxation of the Unconstrained 0-1 Quadratic Programming Problem (QP). Applications of the BQP include mining discrete patterns from binary data,…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…
Quadratic programming (QP) underpins real-time robotics by enabling efficient, constrained optimization in state estimation, motion planning, and control. In legged locomotion and manipulation, essential modules like inverse dynamics, Model…