Hector Ramirez Cabrera

Hector Ramirez Cabrera
University of Chile · Departamento de Ingeniería Matemática

Docteur en Mathématiques Appliquées, École Polytechnique, Palaisseu, France

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78
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657
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March 2015 - present
University of Chile
Position
  • Professor (Associate)

Publications

Publications (78)
Article
Full-text available
In Andreani et al. (Weak notions of nondegeneracy in nonlinear semidefinite programming, 2020), the classical notion of nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely its eigendecomposition. This allows...
Article
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In this note we show with a counter-example that all conditions proposed in Zhang and Zhang (Set-Valued Var. Anal 27:693–712 2019) are not constraint qualifications for second-order cone programming.
Article
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The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constrain...
Preprint
Full-text available
We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with constraint, and another one in terms of a differential inclusion with upper-semi continuous right member but without constrai...
Article
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Preprint
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In [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion of nondegeneracy (or transversality) and Robinson's constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of t...
Article
Full-text available
Nonpharmaceutical interventions (NPI) such as banning public events or instituting lockdowns have been widely applied around the world to control the current COVID-19 pandemic. Typically, this type of intervention is imposed when an epidemiological indicator in a given population exceeds a certain threshold. Then, the nonpharmaceutical intervention...
Preprint
Full-text available
The well known constant rank constraint qualification [Math. Program. Study 21:110-126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this conditio...
Preprint
Full-text available
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global convergence proof of a class of algorithms to stationary points without assuming neither uniqueness of the Lagr...
Article
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This article deals with the inclusion of microbial ecology measurements such as abundances of operational taxonomic units in bioprocess modelling. The first part presents the mathematical analysis of a model that may be framed within the class of Lotka–Volterra models fitted to experimental data in a chemostat setting where a nitrification process...
Article
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Background Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from controlled. People deprived of liberty are a vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow switching to acti...
Preprint
Full-text available
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say, $\ell$-dimensional kernel of the constraint matrix, by the linear independence of a set of $\ell(\ell+1)/2$ derivative vect...
Preprint
Full-text available
Nonpharmaceutical interventions (NPI) such as banning public events or instituting lockdowns have been widely applied around the world to control the current COVID-19 pandemic. Typically, this type of intervention is imposed when an epidemiological indicator in a given population exceeds a certain threshold. Then, the nonpharmaceutical intervention...
Preprint
Full-text available
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first-and second-order algorithms, and for computing the derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualificati...
Preprint
Full-text available
In this note we show with a counterexample that all conditions proposed in [Y. Zhang, L. Zhang, New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs. Set-Valued Var. Anal (2019) 27:693-712] are not constraint qualifications for second-order cone programming.
Preprint
Full-text available
The constant rank constraint qualification introduced by Janin in 1984 for nonlinear programming has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the derivative of the value function. In this note we discuss naive extensions of constant rank type constraint qualification...
Article
Full-text available
We correct Proposition 3.1 of Ref. Haddon et al. (J Optim Theory Appl 183:642, 2019).
Preprint
Full-text available
BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...
Preprint
Full-text available
BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...
Preprint
Full-text available
BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...
Preprint
Full-text available
BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from controlled. People deprived of liberty are a vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow switching to act...
Article
Full-text available
Environmental variability has a strong influence on marine fish stocks. Thus, management and harvest policies based on deterministic indicators, such as maximum sustainable yield (MSY), may be inappropriate facing such uncertainties. In this study, we investigate the long‐term behavior of a single‐species fishery, whose stock is harvested by severa...
Article
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We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the...
Preprint
We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the...
Article
Full-text available
In this paper, we introduce an approach based on viability theory for designing rebuilding programs for overexploited natural resources. Instead of using the so-called viability kernel, as is usual in the applications of viability theory, we consider the set of sustainable thresholds, which represents the constraints (parametrized by thresholds) th...
Preprint
In this manuscript we investigate the long-term behavior of a single-species fishery, which is harvested by several fleets. The time evolution of this population is modeled by a discrete time stochastic age-structured model. We assume that incertitude only affects the recruitment. First, for the deterministic version of this model, we characterize...
Article
In previous works CO2 emissions in oil refineries have been studied for the production units planning. In this manuscript the associated CO2 mitigation costs are added to the scheduling of crude oil unloading and blending. Numerical simulations executed on literature cases show that the optimal scheduling may be affected, thus CO2 emissions may be...
Article
In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramírez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2–30):205–227] for conic optimization problems, and in Peña and Roshchina [A complem...
Article
In this work we study the optimal control problem of maximizing the average biogas production over an infinite horizon. We consider a large class of growth rate functions that depend on substrate and biomass concentrations and we solve this problem for the chemostat model. The obtained optimal control is a autonomous state feedback.
Article
Full-text available
We address the question of mean biomass volumetric productivity optimization, which originates from the simplification of dynamics of microalgae in a batch bioreactor process with light incidence. In particular, the stability of the model is analyzed, some optimality necessary conditions for the nonsmooth optimization problem obtained through the i...
Article
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Microalgae culture fed with ammonium may face the presence of nitrifying bacteria. The aim of this paper is to propose and analyze a nonlinear system which represents XCZthe dynamics of these two species (microalgae and nitrifying bacteria) in competition for nitrogen (present as ammonium and nitrate produced by nitrification) in a continuous proce...
Article
In this work, we revisit a problem of optimal control for the maximisation of biogas production in a continuous bioreactor, for which the analytical determination of the optimal synthesis is an open problem. We consider two kinds of growth rates: substrate dependent or substrate and biomass dependent. We propose a sub-optimal controller, as a most...
Article
In this work we propose a stochastic model for a sequencing-batch reactor (SBR) and for a chemostat. Both models are described by systems of Stochastic Differential Equations (SDEs), which are obtained as limits of suitable Markov Processes characterizing the microscopic behavior. We study the existence of solutions of the obtained equations as wel...
Article
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This paper is devoted to the study of optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the exi...
Article
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We address the problem of the optimal control of in situ decontamination of water resources. We review several modeling, simulation and optimization techniques for this problem and their results. We show the benefit of combining tools from finite dimensional optimal control theory and numerical simulations of hydrodynamics equations, for providing...
Article
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Two gaps were found in the proof of the main theorems (Theorems 21 and 26) of the paper “On the Aubin property of critical points to perturbed second-order cone programs” [SIAM J. Optim. 21 (2011), 3, pp. 798–823] by J. V. Outrata and H. Ramírez C. In this note both these gaps will be filled. As to the second one, a new technical result will be emp...
Article
We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to cons...
Article
This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control prob...
Working Paper
Full-text available
This paper develops a theoretical framework to assess resources management procedures from a sustainability perspective, when resource dynamics is marked by uncertainty. Using stochastic viability, management procedures are ranked according to their probability to achieve economic and ecological constraints over time. This framework is applied to a...
Presentation
Full-text available
MINC (Multiple INteracting Continua) and MRMT (Multiple-Rate Mass Transfer) are mathematical schemes used to modelling transport and difussion in fractured porous media. The main difference between them is the connectivity structure. MINC has a chained type structure (line form) and MRMT has a star-shaped connectivity structure. The goal is show th...
Article
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This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These development...
Article
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The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange m...
Article
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In this note, we correct a mistake in the paper (López et al., J Optim Theory Appl 159(3):741–768, 2013).
Article
Full-text available
This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control prob...
Article
Full-text available
In this paper, we analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics...
Article
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This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). Specifically, our aim is to characterize the class of linear transformations for which the SCLCP has always a nonempty and bounded solution set in terms of larger classes. For this, we introduce a couple of new classes of linear transformations in this...
Article
Full-text available
This paper analyzes feeding strategies in a sequential batch reactor (SBR) with the objective of reaching a given (low) substrate level as quickly as possible for a given volume of water. Inside the SBR, several species compete for a single substrate, which leads to a minimal time control problem in which the control variable is the feeding rate. F...
Article
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In this work we apply multi-class support vector machines (SVMs) and a multi-class stochastic SVM formulation to the classification of fish schools of three species: anchovy, common sardine, and Jack Mackerel, and we compare their performance. The data used come from acoustic measurements in southern-central Chile. These classifications were carrie...
Article
This paper establishes a commutation result for variational problems involving spectral sets and spectral functions. The discussion takes places in the context of a general Euclidean Jordan algebra.
Conference Paper
In this paper we consider the optimal control problem consisting of feeding in minimal time a Sequential Batch Reactors (SBR) where several species compete for a single substrate, with the objective being to reach a given (low) level of the substrate. Following [8, Gajardo et al. Minimal Time Sequential Batch Reactors with Bounded and Impulse Contr...
Article
We study minimal time strategies for the treatment of pollution in large water volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists of feeding the bioreactor from the resource, with clean output returning to the resource with the same flow rate. We first recall recent characterizations of opt...
Article
In this paper we introduce a new class, called F, of linear transformations defined from the space of real n×nn×n symmetric matrices into itself. Within this new class, we show the equivalence between Q- and Qb-transformations. We also provide conditions under which a linear transformation belongs to F. Moreover, this class, when specialized to squ...
Article
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We develop a theoretical framework to assess sheries management strategies from a sustainability perspective, when the bioeconomic dynamics are marked by uncertainty. Using stochastic viability, management strategies are ranked according to their probability to satisfy economic and ecological constraints over time. The proposed framework is useful...
Article
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We characterize the Aubin property of a canonically perturbed KKT system related to the second-order cone programming problem in terms of a strong second-order optimality condition. This condition requires the positive definiteness of a quadratic form, involving the Hessian of the Lagrangian and an extra term, associated with the curvature of the c...
Article
Full-text available
Abstract In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in co...
Article
This paper deals with the control of discrete-time dynamical, monotone both in the state and in the control, in the presence of state and control monotone constraints. A state xx is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from xx and satisfying the constraints. Under monotonicity assumpt...
Article
Full-text available
This work is devoted to the study of existence and stability results of semidefinite linear complementarity problems (SDLCP). Our approach consists of approximating the variational inequality formulation of the SDLCP by a sequence of suitable chosen variational inequalities. This provides particular estimates for the asymptotic cone of the solution...
Working Paper
Full-text available
Les auteurs présentent une nouvelle classe de problèmes de négociations qui peut refléter les problèmes de durabilité recouvrant des enjeux de nature différentes et des problèmes intertemporels. Chaque porteur d'enjeu s'intéresse à l'évolution d'un indicateur dépendant de l'état du système et des décisions, et cherche à maximiser la valeur minimal...
Article
We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate. We first characterize the optimal policies among const...
Working Paper
Full-text available
This paper develops a theoretical framework to assess resources management procedures from a sustainability perspective, when re-source dynamics is marked by uncertainty. Using stochastic viability, management procedures are ranked according to their probability to achieve economic and ecological constraints over time. This frame-work is applied to...
Article
Full-text available
In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular ca...
Working Paper
Full-text available
Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter "acceptable configurations" represent production a...
Article
Full-text available
In this work, we propose an inexact interior proximal type algorithm for solving convex second-order cone programs. This kind of problems consists of minimizing a convex function (possibly nonsmooth) over the intersection of an affine linear space with the Cartesian product of second-order cones. The proposed algorithm uses a distance variable metr...
Article
Full-text available
This paper is devoted to the study of the global asymptotic behavior of a model of chemostat with an arbitrary number of competitors following a Monod law on their specific growth rate functions. The model incorporates discrete time delays in order to take into account the delay in the conversion of nutrient consumed to the viable biomass. In this...
Article
Full-text available
This note deals with a harvesting model for a single stock fishery. In the case of small pelagic fish it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and on fish stock. Empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way to changes in fishing e...
Article
Full-text available
We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy...
Conference Paper
Full-text available
We consider the optimal control problem of feeding in minimal time a tank where several species compete on a single resource. We allow controls to be bounded measurable functions of time as well as impulses. For the one species case, we extend former results given by Moreno to the framework of impulse controls. For the two species case with increas...