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We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
We propose a mixed-integer quadratic programming (QP) solver that is suitable for use in embedded applications, for example, hybrid model predictive control (MPC). The solver is based on the branch-and-bound method, and uses a recently…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
This paper presents an interior point method for pure-state and mixed-constrained optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of…
Task-space quadratic programming (QP) is an elegant approach for controlling robots subject to constraints. Yet, in the case of kinematic-controlled (i.e., high-gains position or velocity) robots, closed-loop QP control scheme can be prone…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
Quadratic programs (QPs) arise in various domains such as machine learning, finance, and control. Recently, learning-enhanced primal-dual hybrid gradient (PDHG) methods have shown great potential in addressing large-scale linear programs;…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
Model Predictive Control (MPC) is a popular optimization-based control technique. MPC is usually formulated as sparse or dense Quadratic Programming (QP). This paper reviews two well-known methods, namely, state condensing and move…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…
In this paper, we propose a combined Magnitude Saturated Adaptive Control (MSAC)-Model Predictive Control (MPC) approach to linear quadratic tracking optimal control problems with parametric uncertainties and input saturation. The proposed…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and a two-sided bound on the 2-norm of its solution. The algorithm minimizes the objective using an active-set method by…