Related papers: Condensed interior-point methods: porting reduced-…
This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
In the last fifteen years a significant progress was achieved by considering an entropic relaxation of the classical multi-partite optimal transport problem (MPOTP). The entropic relaxation gives rise to the rescaling problem of a given…
This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…
We study a tensor optimal transport (TOT) problem for $d\ge 2$ discrete measures. This is a linear programming problem on $d$-tensors. We introduces an interior point method (ipm) for $d$-TOT with a corresponding barrier function. Using a…
Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point…
In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints, called SIPLOG…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where…
While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve a subproblem that aims to minimize a log-barrier penalty…
A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…
In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program,…
A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single CPU core) which reflects the constraints of a bandwidth-dominated…