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Solving Constrained Variational Inequalities via a First-order Interior Point-based Method
[article]
2023
arXiv
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We develop an interior-point approach to solve constrained variational inequality (cVI) problems. ...
ADMM-based interior-point method for constrained VIs (ACVI). ...
(ADMM) 4 ACVI: FIRST-ORDER ADMM-BASED IP METHOD FOR CONSTRAINED VIS 4.1 DERIVING THE ACVI ALGORITHM In this section, we derive an interior-point method for the cVI problem that we refer to as ACVI (ADMM-based ...
arXiv:2206.10575v2
fatcat:3z3c44hs5bflhmpxyzxhivtsne
Large scale inequality constrained optimization and control
1998
IEEE Control Systems
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ince Karmarkar's landmark 1984 paper 13 I], interior point S methods in linear programming have triggered a tremendous amount of activity. ...
In this article, we outline some recent developments in interior point methods for the solution of linear and nonlinear programming problems followed by a summary of the recent work for applying these ...
can be solved readily via interior point methods [57], [76] . ...
doi:10.1109/37.736012
fatcat:jvbmi566mrcdrk5qkkwi7trjla
Page 7804 of Mathematical Reviews Vol. , Issue 95m
[page]
1995
Mathematical Reviews
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of exterior and interior penalty functions are constructed for the variational inequality (1) based on known concepts for the problem (2). ...
The authors present a stochastic method for solving constrained global optimisation problems using a penalty approach. ...
Page 5236 of Mathematical Reviews Vol. , Issue 93i
[page]
1993
Mathematical Reviews
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[Polak, Elijah] (1-CA-C) A generalized quadratic programming-based phase I-phase II method for inequality-constrained optimization. (English summary) Appl. Math. Optim. 26 (1992), no. 3, 223-252. ...
The affine variational inequality problem (AVI) consists in finding a vector x* € X satisfying (Mx*+q,x-—x*)>0 for all xe X where M is a square matrix of order n, X is a polyhedral set in R" and (, ) denotes ...
Fast Evaluation of Quadratic Control-Lyapunov Policy
2011
IEEE Transactions on Control Systems Technology
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For small problems this QP can be solved explicitly; for larger problems an online optimization method can be used. ...
We will show that when the number of inputs is on the order of the square-root of the state dimension, the cost of evaluating a control-Lyapunov policy is on the same order as the cost of evaluating a ...
Many methods can be used to solve the QP (9), including active-set methods, various first-order methods (such as projected gradient), interior-point methods, and explicit analytical solution via multiparametric ...
doi:10.1109/tcst.2010.2056371
fatcat:jeo4eokxyvee3n6o2flci637ay
Page 3700 of Mathematical Reviews Vol. , Issue 2002E
[page]
2002
Mathematical Reviews
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For solving monotone variational inequality problems, Goldstein- Levitin-Polyak’s projection iterative method is among the simplest. ...
The inequality-constrained
problem considered is transformed into an equivalent one by
introducing slack variables and then an interior point approach
is used. ...
Mixed-integer MPC for the temperature control of the batch reactor
2016
MATEC Web of Conferences
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The solver is based on a standard branch-and-bound method and interior point method is used for solution of the relaxed problem. ...
Process controls with a finite number of admissible values are common in a large number of relevant applications. ...
Interior point methods solve the general inequality constrained problem by converting it to an equality constrained problem. ...
doi:10.1051/matecconf/20167602013
fatcat:yi7l2pbuajazlosyzr43glymbi
Page 3061 of Mathematical Reviews Vol. , Issue 2000d
[page]
2000
Mathematical Reviews
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constrained monotone variational inequalities. ...
To our knowledge, this is the first interior-point and infeasible-starting algorithm for solving the MCP that possesses these desired features. Preliminary computa- tional results are presented.” ...
Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems
[article]
2011
arXiv
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Leveraging discrete variational techniques, we construct a family of geometric numerical integration methods that not only obtain the usual desirable properties of momentum preservation, approximate energy ...
To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. ...
In the following sections we will propose the first instantiation of a DELI-based method. ...
arXiv:1007.2233v2
fatcat:e7hjgzu77fchblozhkqftpcgwe
Page 5276 of Mathematical Reviews Vol. , Issue 97H
[page]
1997
Mathematical Reviews
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This paper is one of the first in a number of publications addressing this topic from the viewpoint of interior methods. ...
The programming problem is first formulated as a system of equations using the Fritz John first-order necessary con- ditions and a nonstandard normalization of the multipliers. ...
Spacecraft Trajectory Optimization Based on Discrete Sets of Pseudoimpulses
2009
Journal of Guidance Control and Dynamics
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Indirect methods attempt to solve a two-point boundary-value problem based on the Pontryagin maximum principle [19]. ...
Present-day linear programming methods use interior-point algorithms to solve such problems. ...
doi:10.2514/1.41201
fatcat:f3ac2bqwpvfnhcsb2l54xfsyxy
Inverse electrocardiographic source localization of ischemia: An optimization framework and finite element solution
2013
Journal of Computational Physics
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Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. ...
The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem's specific structure. ...
It approaches the optimal solution via a sequence of interior points (points that are strictly within the subspace dictated by the inequality constraints). ...
doi:10.1016/j.jcp.2013.05.027
pmid:23913980
pmcid:PMC3727301
fatcat:7dy4dwdgizbbff3qs5vjdnj3r4
Trajectory Optimization with Optimization-Based Dynamics
[article]
2023
arXiv
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We provide an interior-point method for efficient evaluation of constrained dynamics and utilize implicit differentiation to compute smooth gradients of this representation. ...
We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem ...
First, in this work we explore constrained optimization problems solved with a second-order method. ...
arXiv:2109.04928v4
fatcat:boqnn3at4baipij23rydxx7qnm
Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems
2012
SIAM Journal on Scientific Computing
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Toward these goals we introduce, for the first time, a fully nonsmooth, discrete Hamilton's principle and obtain an associated framework for composing geometric numerical integration methods for inequality-equality-constrained ...
To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. ...
In the following sections we will propose the first instantiation of a DELI-based method. ...
doi:10.1137/100800105
fatcat:kekkdthjdjcddkofhsjrvp5wvi
On the use of elliptic regularity theory for the numerical solution of variational problems
[article]
2021
arXiv
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stem from contact mechanics leading to elliptic variational inequalities. ...
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. ...
Moreover let an order ≤ defined in Q via a convex closed cone C ⊂ Q via q ≥ 0, iff q ∈ C. ...
arXiv:2101.10440v1
fatcat:gzxocwgfw5e2dn7hdhvkydz7uy
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