Download PDF by Igor V. Konnov, Dinh The Luc, Alexander M. Rubinov: Generalized convexity and related topics

By Igor V. Konnov, Dinh The Luc, Alexander M. Rubinov

ISBN-10: 3540370064

ISBN-13: 9783540370062

ISBN-10: 3540370072

ISBN-13: 9783540370079

The publication comprises invited papers by means of recognized specialists on quite a lot of themes (economics, variational research, chance etc.) heavily on the topic of convexity and generalized convexity, and refereed contributions of experts from the realm on present learn on generalized convexity and purposes, specifically, to optimization, economics and operations examine.

Show description

Read Online or Download Generalized convexity and related topics PDF

Similar linear programming books

Read e-book online Optimal Stopping and Free-Boundary Problems PDF

The booklet goals at disclosing a desirable connection among optimum preventing difficulties in likelihood and free-boundary difficulties in research utilizing minimum instruments and targeting key examples. the final conception of optimum preventing is uncovered on the point of uncomplicated ideas in either discrete and non-stop time masking martingale and Markovian equipment.

Linear Programming and Extensions by George Dantzig PDF

In real-world difficulties with regards to finance, enterprise, and administration, mathematicians and economists usually come across optimization difficulties. First released in 1963, this vintage paintings seems at a wealth of examples and develops linear programming equipment for options. remedies lined contain expense recommendations, transportation difficulties, matrix equipment, and the houses of convex units and linear vector areas.

Kairat T. Mynbaev's Short-Memory Linear Processes and Econometric Applications PDF

This booklet serves as a finished resource of asymptotic effects for econometric versions with deterministic exogenous regressors. Such regressors contain linear (more more often than not, piece-wise polynomial) tendencies, seasonally oscillating services, and slowly various features together with logarithmic tendencies, in addition to a few requirements of spatial matrices within the concept of spatial types.

New PDF release: Robust Discrete Optimization and Its Applications

This publication offers with choice making in environments of vital facts un­ simple task, with specific emphasis on operations and construction administration functions. For such environments, we recommend using the robustness ap­ proach to selection making, which assumes insufficient wisdom of the choice maker concerning the random nation of nature and develops a choice that hedges opposed to the worst contingency which can come up.

Extra info for Generalized convexity and related topics

Example text

Clearly, both the functionals, (13) and (14), are sublinear, and vI′ (c; e′0 ) ≤ ′ vII (c; e′0 ). 1 (see also Remark 1 after it) in [47]. Proposition 5. Given e′0 ∈ dom vI′ (c; ·) := {e′ ∈ E ′ : vI′ (c; e′ ) < +∞}, the following assertions are equivalent: ′ (c; e′0 ); (a) vI′ (c; e′0 ) = vII ′ (b) the functional vII (c; ·) is weakly lower semi-continuous at e′0 . Let us define H := AK; then H 0 = (A∗ )−1 (K 0 ). Remark 3. Note that if dom vI′ (c; ·) ⊆ A∗ C(Ω)∗+ , (15) then, for every e′0 ∈ dom vI′ (c; ·), vI′ (c; e′0 ) = vI (c; µ0 ) and ′ vII (c; e′0 ) = vII (c; µ0 ) / dom vI′ (c; ·), one has whenever µ0 ∈ (A∗ )−1 (e′0 ).

Theorem 4. 1]). A multifunction F : X → L is L-cyclic monotone if and only if Q0 (ϕF ) is nonempty. Theorem 5. 2]). Suppose F : X → L is L-cyclic monotone. Given a function u : Z = dom F → IR ∪ {+∞}, the following statements are equivalent: (a) u ∈ Q0 (ϕF ); (b) u is a restriction to Z of some L-convex function U : X → IR ∪ {+∞}, and F (z) ⊆ ∂L U (z) for all z ∈ Z. Abstract Convexity and the Monge–Kantorovich Duality 51 The next result extending a classical convex analysis theorem due to Rockafellar is an immediate consequence of Theorems 4 and 5.

Abstract Convexity and the Monge–Kantorovich Duality 37 The original program is to maximize the linear functional h, µ0 := h(ω) µ0 (dω) subject to constraints: h ∈ H, h(ω) ≤ c(ω) for all ω ∈ Ω. Ω The optimal value of this program will be denoted as vI (c; µ0 ). , µ ∈ C(Ω)∗+ ) and µ ∈ µ0 − H 0 , where H 0 stands for the conjugate (polar) cone in C(Ω)∗+ , H 0 := {µ ∈ C(Ω)∗ : h, µ ≤ 0 for all h ∈ H}. The optimal value of this program will be denoted as vII (c; µ0 ). Thus, for any µ0 ∈ C(Ω)∗+ , one has vI (c; µ0 ) = sup{ h, µ0 : h ∈ H(c)}, (1) vII (c; µ0 ) = inf{c(µ) : µ ≥ 0, µ ∈ µ0 − H 0 }.

Download PDF sample

Generalized convexity and related topics by Igor V. Konnov, Dinh The Luc, Alexander M. Rubinov

by Charles

Rated 4.83 of 5 – based on 41 votes