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On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control [chapter]

Michael N. Jung, Christian Kirches, Sebastian Sager
2013 Facets of Combinatorial Optimization  
In this article we give an overview over a variety of different modeling approaches, including outer versus inner convexification, generalized disjunctive programming, and vanishing constraints.  ...  In addition to the tightness of the respective relaxations, we also address the issue of constraint qualification and the behavior of computational methods for some formulations.  ...  Complementarity pivoting techniques.  ... 
doi:10.1007/978-3-642-38189-8_16 fatcat:h7ykdvpiafeszn3ycgqpxdhxue

Design Optimization of a Speed Reducer Using Deterministic Techniques

Ming-Hua Lin, Jung-Fa Tsai, Nian-Ze Hu, Shu-Chuan Chang
2013 Mathematical Problems in Engineering  
The original problem is converted by variable transformations and piecewise linearization techniques.  ...  The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem.  ...  Lu and Kim [11] proposed a decomposition algorithm for the multidisciplinary design optimization problems with complementarity constraints based on the regularization technique and inexact penalty decomposition  ... 
doi:10.1155/2013/419043 fatcat:yhfixqwlnvdcjlxs6vjaw3aqzu

Page 2934 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Summary: “A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP).  ...  Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smooth- ing techniques are used to approximate the equality constraint  ... 

Page 4360 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
An optimality criterion for the linear BLPP is derived from two related linear programs constructed by using the complementarity conditions for the second level problem.  ...  For such problems, we have previously presented a generic reformulation-linearization technique (RLT) to obtain global optimal solutions.  ... 

Page 425 of Mathematical Reviews Vol. , Issue 80A [page]

1980 Mathematical Reviews  
Two stronger types of sep- aration (affine and total) are introduced and characterized, for various classes of sets, in terms of extended notions of linear independence and convexifications.  ...  Authors’ summary: “This paper delineates the underlying theory of an efficient method for solving a class of specially-structured linear complementarity problems of potentially very large size.  ... 

A review of recent advances in global optimization

C. A. Floudas, C. E. Gounaris
2008 Journal of Global Optimization  
(2007) studied generalized GGPs in the presence of non-positive variables, proposed a technique for treating these variables, and provided convexification rules for certain signomial terms.  ...  In the first part of this section, we will review the advances in convex envelopes and underestimators, convexification techniques for twice continuously differentiable NLPs, and results regarding concave  ... 
doi:10.1007/s10898-008-9332-8 fatcat:72fpfq72hrdzhf6mxqyc6ssezm

Successive Convexification for 6-DoF Powered Descent Guidance with Compound State-Triggered Constraints [article]

Michael Szmuk, Taylor P. Reynolds, Behcet Acikmese, Mehran Mesbahi, John M. Carson III
2019 arXiv   pre-print
techniques.  ...  This paper introduces a continuous formulation for compound state-triggered constraints, which are generalizations of the recently introduced state-triggered constraints.  ...  Support for studying successive convexification was provided by the Office of Naval Research grants N00014-16-1-2877 and N00014-16-3144.  ... 
arXiv:1901.02181v1 fatcat:2bss5qhin5chzfsoqumudrswcy

A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

Robin Verschueren, Mario Zanon, Rien Quirynen, Moritz Diehl
2017 SIAM Journal on Optimization  
This allows for the use of efficient structure-exploiting QP solvers.  ...  We present a novel regularization method tailored for QPs with optimal control structure. Our approach exhibits three main advantages.  ...  Linear MPC consists in consecutively solving optimal control problems (OCPs) with quadratic objective function, linear dynamics and linear inequality constraints.  ... 
doi:10.1137/16m1081543 fatcat:amxwx4hlcnaghkby2ge3yrwz7m

Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations

Anureet Saxena, Pierre Bonami, Jon Lee
2010 Mathematical programming  
We also propose a new eigen reformulation for MIQCP, and a cut generation technique to strengthen this reformulation using polarity.  ...  We show how the extended formulation can be algorithmically projected to the original space by solving linear programs.  ...  We are grateful to Sam Burer for providing us the box-QP instances and their MIQCP-SDP formulations.  ... 
doi:10.1007/s10107-010-0340-3 fatcat:vajnwliitjcb7mrc4p7dya6jq4

Successive Convexification for Real-Time 6-DoF Powered Descent Guidance with State-Triggered Constraints [article]

Michael Szmuk, Taylor P. Reynolds, Behcet Acikmese
2018 arXiv   pre-print
In this paper, we present a real-time successive convexification algorithm for a generalized free-final-time 6-degree-of-freedom powered descent guidance problem.  ...  and range-triggered line of sight constraints.  ...  For a given z, (17a) forms a linear complementarity problem (LCP) in σ [40] . This problem has a unique solution σ that varies continuously in g(z) [40] , and therefore in z.  ... 
arXiv:1811.10803v1 fatcat:lxsq76742jh33f7g54j4qzbame

Advances in Trajectory Optimization for Space Vehicle Control [article]

Danylo Malyuta, Yue Yu, Purnanand Elango, Behcet Acikmese
2021 arXiv   pre-print
The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites.  ...  The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming  ...  The authors would like to extend their gratitude to Yuanqi Mao for his helpful inputs on sequential convex programming algorithms, and  ... 
arXiv:2108.02335v2 fatcat:g5peodqyj5b23g347zybbfulxi

How to solve a semi-infinite optimization problem

Oliver Stein
2012 European Journal of Operational Research  
Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive  ...  convexification procedures.  ...  In fact, each scalar complementarity constraint 0 ≤ −v (x, y) ⊥ γ ≥ 0, = 1, . . . , s, is first equivalently replaced by the equation ψ(−v (x, y), γ ) = 0 with a complementarity function ψ like the natural  ... 
doi:10.1016/j.ejor.2012.06.009 fatcat:wqtoipg2aff3tn67boq2owmhta

Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations

Anureet Saxena, Pierre Bonami, Jon Lee
2010 Mathematical programming  
In particular, we propose new methods for generating valid inequalities by using the equation Y = xx T . We use the concave constraint 0 Y − xx T to derive disjunctions of two types.  ...  To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-and-project methodology.  ...  Thanks to Sam Burer for providing the box-QP instances, and for a productive discussion which eventually helped us to (re)discover Theorem 2.  ... 
doi:10.1007/s10107-010-0371-9 fatcat:w4c5rkcadrh4po6bsj7lgeiqrm

Book announcements

2000 Discrete Applied Mathematics  
Rinaldi Active set algorithm based on null space of the constraints 3 Active set algorithm based on range space of the constraints Properties of the method: linear equality constraints 4 Revealed preferences  ...  1.3.7 Linear complementarity problem (LCP) 1.3.8 Positive semi-definite programming (PSP) 1.3.9 Nonlinear programming (NP) 1.3.10 Nonlinear complementarity problem (NCP) 1.4 Algorithms  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Ideal formulations for constrained convex optimization problems with indicator variables [article]

Linchuan Wei, Andres Gomez, Simge Kucukyavuz
2021 arXiv   pre-print
As special cases of this result, we derive ideal convexifications for problems with hierarchy, multi-collinearity, and sparsity constraints.  ...  Moreover, we also give a short proof that for a separable objective function, the perspective reformulation is ideal independent from the constraints of the problem.  ...  Results Conclusions In this paper, we propose a unifying convexification technique for the epigraphs of a class of convex functions with indicator variables constrained to certain polyhedral sets.  ... 
arXiv:2007.00107v2 fatcat:oz3mglvdiba3dad2djo54bk3sm
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