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Invex optimization revisited

Ksenia Bestuzheva, Hassan Hijazi
2018 Journal of Global Optimization  
In this work, we provide necessary conditions for KT-invexity in n dimensions and show that these conditions become sufficient in the two-dimensional case.  ...  Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer.  ...  Definition 4 (Weak boundary-invexity) Problem (NLP) is weakly boundary-invex if for every i that corresponds to a non-convex constraint either the problem (NLP i ) does not have a finite global optimal  ... 
doi:10.1007/s10898-018-0650-1 fatcat:rhtph6l5vbaozb4duqkyiotsmm

Invex Optimization Revisited [article]

Ksenia Bestuzheva, Hassan Hijazi
2017 pre-print
This property is known as KT-invexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer.  ...  Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer.  ...  One such property, called Kuhn-Tucker invexity, is the sufficiency of KKT conditions for global optimality: Definition 1 [14] An optimization problem is said to be Kuhn-Tucker invex (KT-invex) if every  ... 
doi:10.13140/rg.2.2.22438.83529 arXiv:1707.01554v1 fatcat:hxxa2s6cbjgtrf3bnsxujqaa5a

Page 9761 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Petersburg) Minmaxmin problems revisited. (English summary) Optim. Methods Softw. 17 (2002), no. 5, 783-804.  ...  Summary: “Global invexity is characterized by a condition which is independent of the scale function describing the invexity.  ... 

On sufficient optimality conditions for multiobjective control problems

Valeriano Antunes de Oliveira, Geraldo Nunes Silva
2015 Journal of Global Optimization  
Non-regular optimization problems were studied in . The concept of KT-invexity was brought to the optimal control context in de Oliveira, Silva and Rojas-Medar [23] and Arana et al. [4, 5] .  ...  In 1985, Martin [41] redesigned Hanson's notion of invexity, while maintaining the sufficiency of the Kuhn-Tucker conditions. This generalized concept of invexity was termed KT-invexity.  ...  We now revisit Example 1.  ... 
doi:10.1007/s10898-015-0351-y fatcat:w6o5sd6yknbzvlbwopuchnkdcm

Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints

Iqbal Husain, Vikas K. Jain
2013 Open Journal of Modelling and Simulation  
As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-Weir type dual to this problem is formulated and various duality results are established under generalized invexity assumptions  ...  In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function  ...  T z h is quasi-invex.  ... 
doi:10.4236/ojmsi.2013.12002 fatcat:dblzdh5fqjeozplpbozlvi3f6a

Page 1200 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Kiwiel (PL-PAN-S) 91b:90171 90C29 White, Douglas John (1-VA-E) Least elements revisited. J. Optim. Theory Appl. 65 (1990), no. 1, 117-128.  ...  Kuhn-Tucker necessary conditions are obtained, which are also sufficient if f is Q-invex and g is S-invex with respect to the same function n:X x X — X (in the sense of the author [Bull. Austral.  ... 

Generalisations, Examples, and Counter-examples in Analysis and Optimisation

Jonathan M. Borwein
2016 Set-Valued and Variational Analysis  
In the following section I will then revisit corresponding examples for these results.  ...  Example 3.9 (Invexity II). Finally let us observe that invex problems have no useful permanence properties.  ... 
doi:10.1007/s11228-016-0379-2 fatcat:sorawl42l5fqjmunbvrpfyz5um

Page 2358 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
Applications of the general definitions are studied in terms of invexity and B-vexity.” 2000c:90059 90C26 90C46 Ye, J. J.  ...  proof benefits from the insight gained on a new class of hy- perplanes and its associated simplicial lower bound, recently developed by the authors [“The simplicial lower bound for conical algorithm revisited  ... 

Page 1572 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Miglierina, Invex functions on differentiable manifolds (299-311); F. Mignanego and G.  ...  -functions revisited (179-219); Luca Grosset and Bruno Viscolani, Advertising and price for a ser- vice subject to congestion (221-230); Sandor Komldsi, On the Stampacchia and Minty variational inequalities  ... 

Page 2715 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Minmaxmin problems revisited. (English summary) 2003m:90155 Dem’yanoy, V. F. see Demyanoy, A.  ...  (English summary) 2003¢:49063 Bhatia, Davinder (with Sharma, Arpana) New-invexity type conditions with applications 2003k:49076 Bigi, Giancarlo Saddlepoint optimality criteria in vector optimization.  ... 

Page 1054 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
Kim, Do Sang Optimality and duality for multiobjective variational problems with invexity. — (with Lee, Gue Myung; Kuk, Hun) Duality for nonlinear multiobjective fractional variational problems.  ...  Optimality and duality for variational problems with generalized convexity. (English summary) 99b:90112 Nahak, Chandal On multiobjective generalized symmetric dual programs with p-(, 0)- invexity.  ... 

Page 2503 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
Duality for optimal control-approximation problems with gauges. (English summary) 2000g:49039 White, Douglas John Lagrangean relaxation revisited, technical note.  ...  (English summary) Bhatia, Davinder (with Mehra, Aparna) Optimality conditions and duality for multiobjec- tive variational problems with generalized B-invexity.  ... 

Analysis of closed-loop inertial gradient dynamics [article]

Subhransu S. Bhattacharjee, Ian R. Petersen
2022 arXiv   pre-print
Under the additional assumption of invexity, we establish a momentum-driven adaptive convergence rate.  ...  We revisit classical problems in optimization theory, which form the heart of popular deep learning algorithms.  ...  Unlike other optimization methods, we use a black-box model of optimization which yields the gradient of the cost function only at the point of the query.  ... 
arXiv:2203.02140v2 fatcat:xx43m2brard55ifk47hw6phisq

Fixed-Time Convergence for a Class of Nonconvex-Nonconcave Min-Max Problems [article]

Kunal Garg, Mayank Baranwal
2022 arXiv   pre-print
In particular, it is shown that by leveraging the dynamical systems viewpoint of an optimization algorithm, accelerated convergence to a saddle point can be obtained.  ...  Recall that h y (x) is a positive invex function bounded from below by 0, while the derivative ∇ x h y (x), too, is bounded from below by a positive constant.  ...  Revisiting (14) , we obtain: h y (x 0 ) − h y (x(T )) = T 0 ∇ x h y (x) 2 dt (14) ≥ µ 1 2 T 0 ∇ x h y (x) dt (15) ≥ µ 1 2 x 0 − x(y) . (16) Fig. 1 . 1 Fig. 1.  ... 
arXiv:2207.12845v1 fatcat:x3qpnm4e7ram7n3oxtdkqjdr7m

Author Index, Volume 51 (1995) – 60 (1999)

1999 Bulletin of the Australian Mathematical Society  
Rubin Elementary Abelian p-groups revisited 52 (1995) 373 Zhangjian Hu Admissible limits of block functions on bounded strongly pseudoconvex domains 54 (1996) 1 Zhibao Hu, Warren B.  ...  Nanda Semi-invex functions and their subdifferentials 56 (1997) 385 D. Easdown and W.D. Munn Irace function on inverse semigroup algebras 52 (1995) 359 L-J. Eaton see K.J.  ... 
doi:10.1017/s0004972700036698 fatcat:yl24tfr5bbekdcfctcpzk54ws4
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