Related papers: Combining the regularization strategy and the SQP …
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
Multimodal planning capabilities refer to the ability to predict, reason, and design steps for task execution with multimodal context, which is essential for complex reasoning and decision-making across multiple steps. However, current…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
In a Mathematical Program with Generalized Complementarity Constraints (MPGCC), complementarity relationships are imposed between each pair of variable blocks. MPGCC includes the traditional Mathematical Program with Complementarity…
Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…
In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…
This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation.…
We consider a degenerate nonsmooth and nonconvex optimization problem for which the standard constraint qualification such as the generalized Mangasarian Fromovitz constraint qualification (GMFCQ) may not hold. We use smoothing functions…
This paper focuses on developing effective algorithms for solving bilevel program. The most popular approach is to replace the lower-level problem by its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity…
This paper presents the Julia package CCOpt, built on top of the interior-point solver MadNLP. CCOpt implements a suite of algorithms for Mathematical Programs with Complementarity Constraints (MPCCs). The solver additionally comes with…
Model Predictive Control (MPC) is a successful control methodology, which is applied to increasingly complex systems. However, real-time feasibility of MPC can be challenging for complex systems, certainly when an (extremely) large number…
This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality…
This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for…
Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor…
In this workshop, we present a compact but rigorous introduction to the basic language of nonlinear programming, variational inequalities, and complementarity systems. The goal is twofold. First, we explain the mathematical logic of…
We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a…