Related papers: Optimality conditions and constraint qualification…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
This paper proposes a novel constraint-handling mechanism named angle-based constrained dominance principle (ACDP) embedded in a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective…
For bilevel programs with a convex lower level program, the classical approach replaces the lower level program with its Karush-Kuhn-Tucker condition and solve the resulting mathematical program with complementarity constraint (MPCC). It is…
The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity (BBC)…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Difference-of-Convex (DC) minimization, referring to the problem of minimizing the difference of two convex functions, has been found rich applications in statistical learning and studied extensively for decades. However, existing methods…
This paper is devoted to the study of the metric subregularity constraint qualification (MSCQ) for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and…
We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of…
This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, \maxcut is a boolean CSP where the input is a graph $G = (V,E)$ and the goal is to find a cut…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
The $k$-Maximum Dispersion Problem with Cardinality Constraints ($k$-MDCC) asks for a partition of a given item set with pairwise dissimilarities into $k$ cardinality-constrained groups such that the minimum pairwise intra-group…
Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…
We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a…
This paper aims to provide a Dynamic Programming (DP) approach to solve the Mission-Wide Chance-Constrained Optimal Control Problems (MWCC-OCP). The mission-wide chance constraint guarantees that the probability that the entire state…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random…